Because of tailbone problem I use special cushion that works perfectly in 2001 Park Avenue. Problem. Seats are always being changed. Is it possible to have a) Manufacturer install 2001 type seats in a new car? b) Install my 2001 seats in a new car?

The assembly line would never customize a new car that way. That kind of adaptation for your needs would have to be after the purchase but sounds 100% do-able either by the new car dealer ( as they customize new cars with rims, stripes, sound systems, lift kits etc ) or by an accessabilty shop ( “handicap” hand controls, hoists etc. ).

If the new car is equipped with the type of head restraints that move and adapt to impact forces in order to protect the passengers’ heads, the dealer would be unable to swap old seats into the car. Just as anti-pollution equipment cannot be disconnected, the dealer would get into a whole heap of legal trouble if he was to remove safety equipment from a new car. An after-market shop may be willing to do something like this, but I seriously doubt if a new car dealer would do it.

Please be a little clearer in your post… do you use a special bottom cushion that replaces the one that came with your car, or is this an additional cushion that you can take with you from car to car, and happens to fit very well in an 01 Park Ave?

I am in the same boat as you will tailbone pain.
I found when switching cars you need to modify your cushion. The new car seat may be lower in the front so you will build up front of cushion. Take carpet padding and cut to size, untill you get it right you can use double sided tape or string, whatever you can come up with to hold it in place.
It will take a few tries of different padding and thickness to get it right, when you do then you can use glue to keep it secure. There are all kinds of foam check around.
I tried 6 different computer chairs before getting the right on and 4 different cushions and use about 7-8 layers of carpet padding under it.
The best cushion I found are in a catolog called dr leonard. It is not slanted and have a layer if dense foam then gel then more foam. In my 97 rav4 I use a slanted solid dense foam, had to build up the center of cushion on that one.
I am on disability mainly because of tailbone and can ride about 80mi instead of 50 in a day before really hurting. Can set 3 hrs instead or 1.5-2 before having to lay down.

Its all trail and error hope this helps