Hello and welcome to JustAnswer.com!

First off contact your local Toyota dealer. There is a recall on some of the engine computers on these which can cause idle issues and stalling. They will be able to run your VIN to see if your car is one of the affected vehicles (or if the recall has already been done).

These are bad for a small leak at the intake manifold gasket causing excessive engine vibration. In extreme cases it can also make the check engine light come on. Toyota came out with an updated thicker gasket for this problem (Part # XXXXX).

You can also try cleaning the mass air flow sensor and the throttle body. When these get dirty idle can be affected. A change of idle as low as 20-30rpm below normal can cause excessive vibration.

These are known for the belt tensioner causing vibration but his is usually more of a noise and less of a vibration you can feel. I don't think this is your problem.

You said your mechanic replaced the mounts. Did he replace the top passenger side mount as well? This is usually the root of vibration problems. Toyota has an updated part number of #12305-0D120 for this mount to address engine vibration issues.

Also new spark plugs can make a big difference on these. Toyota says they don't need to be replaced until 120,000 miles but in reality by 100,000 they are pretty well worn out.