A T-Tech fluid exchange will remove ALL of the old fluid if enough new fluid is used.
Your transmission shop is confusing neglected transmissions with yours.
If your transmission filter was full of sludge, and the fluid had never been changed, then I could see how a complete fluid exchange with new fluid can cause problems, as the new fluid would break down deposits (and sludge) from parts and clog up the filter.
This isn't the case. Your filter is clean, I assume. You've done four or five pan drops, so the fluid is already quite clean. While 4-5 drain/fills may dilute MOST of the old fluid, if one runs enough (18 quarts) of new fluid through all at once with a machine, you can remove all of it.
There are many different types of transmission fluid exchange services.
One is by BG. It uses a cleaner and conditioner, followed by a flush. It has the capability of breaking down deposits. Some claim it's a backflush, I don't know.
Then there's the T-Tech, which is probably the most popular. It uses nothing but new fluid, and puts no pressure on the transmission. In fact, the machine runs entirely off the transmission pump, so no "extra" pressure is put on the unit. This is the machine Jiffy Lubes use, so I really cannot see how a problem can occur.
Then Wynn makes another one that uses cleaners and conditioners. Don't know much about it other than that.
The Pennzoil Multi-Vehicle is compatible with SP-III applications, at least according to the data sheet and their technical support department.
Amsoil also makes a good product that'll work in SP-III, and our sponsorer Specialty Formulations also makes one.
If your transmission is already experiencing shifting problems, I'd have the T-Tech done and reset the TCM and hope for the best. It won't cause any additional problems, at best, it may buy you additional time if it doesn't solve the problem.
FazerZ on this forum is in Matthews and could rebuild your transmission if you ever need it done. (Hopefully not)