Before you do anything drop that transmission pan!!!
Shifting and performance problems are like this are often caused by low fluid pressure due to a clogged filter. In my experience, a fluid and filter change along with a pan cleanout will fix the problem about 50% of the time.
Yes, I know you had a trans flush. This kind of service does nothing to free-up a clogged filter and nothing to clean out a pan. IMHO these services are misleading to consumers and are pushed onto customers mostly because it is a quick, easy, high- profit service that mechanics can easily sell to consumers.
Regular (every 3 years or so) transmission filter and fluid change (where the pan is dropped and cleaned out) is MUCH more useful in maintaining a transmission than a flush.
Drop the pan and take a look. A modest amount of friction material and dirt (dark grey debris) in the pan is normal. However, if there is lots of it, your filter may be packed solid and not allowing fluid to flow, thus causing your problem.
In my opinion, new fluid, filter and gasket may work. It's cheap and easy to do and imo worth a shot before you get wrapped up in a transmission change. If you do this, drive the car for a while, to make sure that any lingering debris in the trans gets flushed out.
If you do the swap, definitely get a Haynes or Chilton service manual to show you what to do. It's a big job with
many different steps involved... some of which may not be immediately obvious. It's dangerous too, if you do not know what you are doing.
Among the unusual steps involved, you have to support the engine from above, by chaining it to a 2x4 wooden bar that you have to cut and fit so it rests on the strut towers.
You have to unbolt the front struts so you can get the driveshafts out of the trans before removal. You must mark the strut location on the steering knuckle, or else you will be doing an alignment afterwards.
As for transmission compatibility, the wrecking yard can take care of this. They should have a Hollander Interchange manual (or software) that tells them what other transmissions will fit. Ask them to see their copy of the manual to be sure, if you have any doubts.
There are many minor differences between years, and even within the same year of car, so it's best to let them look after finding you a compatible one.
And finally..... good luck!