Sorry, can't help with the uneven heating from the steering area. I don't have my car with me at the moment, but I do not recall the pop-out controls for the mirrors, etc, to feel particularly warm either.
As for the 60k service, it's pretty much the full service that you see in your service handbook + spark plugs. The spark plugs are Denso FK20HBR11, such as these.
A reputable independent should be able to take on the 60k service. However, looking at the myriad of problems that you are facing, a Lexus dealer may be able to troubleshoot it better (just a guess). Plus they do a hybrid health check and give you a year's warranty on the battery.