I got the trailer to a dealer that charged me for an hours work and said the black tank drained just fine. The service manager gave me some advice to wait for the tank to be full to drain it the next time. Also to use Aqua-Kem, two bottles this next tank full. So I did as he said. It has been more than two week since I got the trailer back and my sink was making gurgling sounds this morning so I decided to try to drain the black tank too. Sure enough it won't drain. There was a little drainage but it quit pretty quick.
I hooked up my trailer to the pickup and towed it over some fairly rough road and up/down some hilly roads. No luck. Then I got the idea to try one of those reverse flush adapters that allow a garden hose to add water to the tank thinking it might open up the drain. It was a Rhino tank rinser from Camco. It leaks at the lower joint on all sides. I tried to make a gasket out of Press and Seal kitchen wrap. This actually worked but it still had some leaking.
Tomorrow I'll go back to the same dealer, schedule another shop visit and ask about the rinser they sell. Next time I get my tank to drain again I'm going to do a lot of flushing of the black tank. It's a good thing I'm recently retired because I wouldn't have time for all this if I had to maintain a job.