First and foremost drop the idea of a flush. When most tech shops perform a flush they do a high-pressure flush by putting a compressor line on the filler neck and then letting things rip. It is true that this will blast anything within the transmission cover out and into the pan. However, it is equally true that it may dislodge major deposits that have built up on, say, turbine blades or various surfaces. As the little chunks move around, they can damage some of the more delicate parts like check valves and such. Further, the chunks can become lodged in tiny galleries, causing heat problems or in the valve body valves themselves, causing shifting problems.
I can see where it might seem like the problem is in the solenoids alone. In fact, I can also agree that the diagnostic scanner would return the results that it returned. Further, if your tech has repaired Solenoids 1 and 2, the next obvious result codes you would receive, of course, would show that 3 and 4 have to be repaired.
However, I also think your technician is onto something with the valve body. You said that the Caddy hadn’t been driven in a year and that when you changed the transmission fluid it was black. Of course, that would be the case. However, that blackness also indicates a lot of dirt and possible buildups may be inside the transmission and when you keyed it on the first time, it is likely they spread throughout the transmission, resulting in problems that might not show up in error codes.
If the valve body has problems because one or more valves in a train of devices for a specific gear is stuck, it can force your transmission to mimic poor torque converter operation, which can also be indicated by the way your transmission is operating. Indeed, with the solenoid error codes, the valve body problem seems to make more and more sense.
With that said, I would have the valve body dismounted and thoroughly cleaned. I would also have the check valves either reset or replaced. I think that should fix your Caddy right up and you’ll be on your way. Let me know the results of this as I have some other thoughts, however, I don’t want to make things overly ambitious and costly for you. Like as not this will fix your Caddy right up.