No, the air cleaner housing is not after market but original. Only the filter is after market. There is no contact between the air cleaner housing and the carburetor other than normal.

Well, that is not clear to me. Hard to see.

When cold and working properly, the high idle is at 1,500 rpm while the low idle is at 1,000 rpm. The issue I have is that it goes to 2,000 rpm and sticks there when hot. Sometime I managed to make it drop down to 1,500 rpm by taping the gas pedal. It is as if it was adding 500 rpm at both low and high idle, when hot.

From the description of the issue, it sounds like the throttle blade shaft(s), and/or bores for them in the baseplate might be worn. I've also seen the base gasket hang the throttle blades if it becomes distorted/damaged, or is not properly cut when it is made. The gasket between the baseplate and the carb fuel bowl can also be distorted and hang the throttle blades.  With the air cleaner completely off, and the car idling hot, see if you can manually push the throttle linkage(right where the cable is attached) forward to lower the idle speed. Wiggle up/down the linkage(on the carb itself) and see if the idle changes as you wiggle. This would indicate a worn shaft or bore. 

dam spelchek

I have replaced a lot of throttle body plates due to the wear problem.  In addition to what Joel has said, with the engine off open the throttle a few degrees and then try to lift the throttle link up and down and front to rear.  A SLIGHT movement is okay but anything else is an indication of a worn shaft and or bushings.   The plate can be rebuilt, but it may be hard to find someone competent to do the rebuild/repair.  You may need to just replace the throttle plate.  Make sure it's an exact match or  you will be installing other problems you don't want.

Here's a good place to get it rebuilt or parts for it.  https://cliffshighperformance.com/