Compressors are generally inefficient at low RPM, so the R134 refrigerant level has to be right or it won't cool well. If you've had both of these addressed and it still isn't working right, the next up would be the expansion valve. Something might be clogging it and it just can't deliver the spray of liquid into the evaporator at lower line pressures.
If you take out the glove box and reach up and to the left the expansion valve and it's fittings are visible. But it's tight packaging and I don't know if it's possible to replace it without tearing down the entire dash.
The Limited is fully electronically controlled and does have a set of DTC codes. But you'll need a scanner that can handle proprietary codes in order to view them. A fully equipped HVAC shop might be able to do it for you, or you'll have to visit Toyota.
Another possibility is that the cold air is being diluted by some heat from the heater core. There's no valve on the hot water lines, so the core is always hot. If the airmix damper wasn't fully closing within the HVAC box, it's possible that at lower RPM the AC is being swamped out by the heater.
If you take out the glove box and reach up and to the left the expansion valve and it's fittings are visible. But it's tight packaging and I don't know if it's possible to replace it without tearing down the entire dash.
The Limited is fully electronically controlled and does have a set of DTC codes. But you'll need a scanner that can handle proprietary codes in order to view them. A fully equipped HVAC shop might be able to do it for you, or you'll have to visit Toyota.
Another possibility is that the cold air is being diluted by some heat from the heater core. There's no valve on the hot water lines, so the core is always hot. If the airmix damper wasn't fully closing within the HVAC box, it's possible that at lower RPM the AC is being swamped out by the heater.