OK, we have to take a few steps backwards... I don't mean to be critical, but I have to say two things before addressing your issue. First, STOP clearing the codes! If the problem is fixed, the light will go out on its own. THEN you can clear the codes. All code-clearing does is cause problems for the next guy who works on the car. Next, DIAGNOSE the problem before throwing any more parts at it! At this point, you've thrown so much at it that you may have actually created new problems that manifest like the old problems.
Now, on to you actual issue... P0420/P0430 happen for 2 reasons. The sensors that detect the levels of oxygen in your post-cat exhaust are bad OR your engine is having incomplete combustion causing the post-cat O2 sensors to detect an actual issue. Your engine could be running lean or rich. Either can cause incomplete combustion. Now, the key indicators are that both cats are showing issues (indicating an engine/combustion issue) AND you say there are random misfires occurring. I'd like to know some history. Were you getting these codes and then you started on this parts cannon journey or were the random misfires first and then you got these codes? How is your gas mileage? Does the engine run smoothly? Did you have any work done (i.e. timing belt) done within a few months before this issue popped up?
As for possible sources of the issue, the best approach is to step back and look at the problem from a distance. The problem IS incomplete combustion. So, the 3 things that can cause incomplete combustion are fuel, air and spark. You haven't said your mileage, but, have you had all the recommended service (timing belt, spark plugs, etc.) done at recommended intervals? For fuel trims, you should get 4 numbers for bank 1 short term, bank 1 long term, bank 2 short term and bank 2 long term. The long term numbers are what matters most. Those should be as close to zero as possible, but something like +/- 6 is probably ok. You also want to check the O2 values, which should be 2 different numbers. Bank 1 Sensor 2 and Bank 2 Sensor 2. I've also seen something like "Front-Downstream," depending on the software. You want to capture these on a graph. They should bounce between 0.1 and 0.9 volts. However, these values only really matter AFTER the car is warmed up.
Given that you replaced a bunch of stuff and didn't fix the issue, I'm going to hope that those parts are now all OK and pick from what's left. The answers to my questions above will change what might or might not be the issue. I would check the fuel pressure. If your pressure is too low or too high, that would indicate a fuel pump issue. Next up would be that I would search for vacuum leaks. To be thorough, you need a smoke tester, but a visual inspection of all lines and the starter fluid test around any potential leaks (i.e. throttle body, valve cover, etc.) would probably be a decent start. Since your in diagnostic mode, I would ALSO check the battery level, alternator output, and that all connections are clean and tight and jiggling hot or ground cable doesn't cause misfires. After that, I would consider the spark plugs, especially if your fuel trims are close to zero. If you've got 80k miles since the last plug change or used something other than the super-expensive iridium Denso or NGK plugs, that would probably be the suspect component for me. A dirty throttle body, or leaking TB gasket, valve cover gasket or intake manifold leak could also come in here, and should all be done at the same time as a spark plug change, so you might as well do all at the same time. Now, after that, there are some other misc suspect elements. A heavily clogged PCV could cause issues, but usually would manifest with a rotten-egg smell when under load (i.e. going uphill) at highway speeds. A worn timing belt or one that has advanced or retarded by "slipping a tooth" could cause combustion issues. A blown head gasket could (unlikely) cause issues with water vapor in the exhaust, so monitored, stable coolant levels and checking the oil condition to make sure it hasn't turned to engine butter would be good checks. Checking the coolant for exhaust gasses could also be in order here too. If all of that checks out or can be eliminated, we get into the far less likely but possible territory like a number of micro-issues adding up to a large issue or a part that essentially never fails failing or some weird assumed unrelated issue (i.e. transmission issues) that was overlooked because it was assumed to not be the issue.
Now, on to you actual issue... P0420/P0430 happen for 2 reasons. The sensors that detect the levels of oxygen in your post-cat exhaust are bad OR your engine is having incomplete combustion causing the post-cat O2 sensors to detect an actual issue. Your engine could be running lean or rich. Either can cause incomplete combustion. Now, the key indicators are that both cats are showing issues (indicating an engine/combustion issue) AND you say there are random misfires occurring. I'd like to know some history. Were you getting these codes and then you started on this parts cannon journey or were the random misfires first and then you got these codes? How is your gas mileage? Does the engine run smoothly? Did you have any work done (i.e. timing belt) done within a few months before this issue popped up?
As for possible sources of the issue, the best approach is to step back and look at the problem from a distance. The problem IS incomplete combustion. So, the 3 things that can cause incomplete combustion are fuel, air and spark. You haven't said your mileage, but, have you had all the recommended service (timing belt, spark plugs, etc.) done at recommended intervals? For fuel trims, you should get 4 numbers for bank 1 short term, bank 1 long term, bank 2 short term and bank 2 long term. The long term numbers are what matters most. Those should be as close to zero as possible, but something like +/- 6 is probably ok. You also want to check the O2 values, which should be 2 different numbers. Bank 1 Sensor 2 and Bank 2 Sensor 2. I've also seen something like "Front-Downstream," depending on the software. You want to capture these on a graph. They should bounce between 0.1 and 0.9 volts. However, these values only really matter AFTER the car is warmed up.
Given that you replaced a bunch of stuff and didn't fix the issue, I'm going to hope that those parts are now all OK and pick from what's left. The answers to my questions above will change what might or might not be the issue. I would check the fuel pressure. If your pressure is too low or too high, that would indicate a fuel pump issue. Next up would be that I would search for vacuum leaks. To be thorough, you need a smoke tester, but a visual inspection of all lines and the starter fluid test around any potential leaks (i.e. throttle body, valve cover, etc.) would probably be a decent start. Since your in diagnostic mode, I would ALSO check the battery level, alternator output, and that all connections are clean and tight and jiggling hot or ground cable doesn't cause misfires. After that, I would consider the spark plugs, especially if your fuel trims are close to zero. If you've got 80k miles since the last plug change or used something other than the super-expensive iridium Denso or NGK plugs, that would probably be the suspect component for me. A dirty throttle body, or leaking TB gasket, valve cover gasket or intake manifold leak could also come in here, and should all be done at the same time as a spark plug change, so you might as well do all at the same time. Now, after that, there are some other misc suspect elements. A heavily clogged PCV could cause issues, but usually would manifest with a rotten-egg smell when under load (i.e. going uphill) at highway speeds. A worn timing belt or one that has advanced or retarded by "slipping a tooth" could cause combustion issues. A blown head gasket could (unlikely) cause issues with water vapor in the exhaust, so monitored, stable coolant levels and checking the oil condition to make sure it hasn't turned to engine butter would be good checks. Checking the coolant for exhaust gasses could also be in order here too. If all of that checks out or can be eliminated, we get into the far less likely but possible territory like a number of micro-issues adding up to a large issue or a part that essentially never fails failing or some weird assumed unrelated issue (i.e. transmission issues) that was overlooked because it was assumed to not be the issue.