The Riv's OBD 1.5 is basically OBD I reading thru an OBD 2 connector. .
If you are near a major city it should not be too hard to find a shop (other than a dealer) with the ability to scan the Riv. Also there is already a thread on scanners that will work. A GM dealer's Tech II will work.
Do not be surprised if the chain transmission shops have such scanners. Do not be surprised if the chains such as Goodyear and Firestone car care centers have them too - you might phone and ask. Also, do not be surprised if for a half hour's labor (or so) a GM dealer will "check and advise" concerning your issue. Finally, do not be surprised to find that many mechanics do not like to diagnose/repair electrical problems.
I am not a transmission specialist but i will "think out loud" about this one...
One, I am beginning to wonder if your car has a bunch of little vacuum leaks. If the rubber connectors at the vacuum tree (on top of engine) or at the various vac points have hardened odds are they leak, too. That alone will mess up your shifting.
Secondly, please carefully check the electrical connectors on the transmission for wires that have fatigued and broken inside the insulation. If you do not know how to check for this please post and say so.
Third, if your mechanic can make the transmission shift with the scanner, then you most likely do not have a problem with the solenoids and unless you find an external electrical problem is the cause then the transmission needs to be removed and opened for inspection. The parts to rebuild it while not free are not a fortune - the labor is what gets you on the transmission R&R. Your mechanic probably does not want to tear into the transmission, and the average transmission shop wants to put in a used or rebuilt transmission. If you are near a major city you might want to find a shop that actually rebuilds transmissions for the trade, limp over there for the diagnosis and repair if in fact that's the problem.
Fourth, I wonder if a sensor has gone bad - no way to tell without the scanner but just a thought.
Fifth, I wonder if there is transmission fluid inside the modulator (in which case, it's sprung a leak). If so it needs to be replaced.