Well, sometimes, if you listen carefully, the universe speaks to you.
While getting ready to pull the boat from the 'back forty' to the front of the property to fire her up, I discovered that the steering wouldn't budge. The cable is frozen, so I'll replace that and the 'helm', per the advice of my mechanic back in Detroit. I did stand on the cavitation plate and there was no flex, just the trailer sagging under the weight. While tapping on the outside of the transom, things seemed to be o.k., but it seems to me there's just a little bit of an art to that, given the different tones that can be generated depending on where internal support structures are. On the inside, a bit of a different story. In the photo below, the 'hatched' areas in chalk are solid, and just happen to be, I'm guessing, on top of internal framing. Most of everything else was soft to the touch. I'm guess the outer layers on the inside half of the transom have delaminated or rotted.
With the start of the season of the sport that I was the long-time president of tomorrow, and given the good advice of everyone involved here, my boating season is done. I'll focus on the repair process over the winter / spring, and give the resources on this site a good going over. Btw, the sport, arguably North America's most obscure, is featherbowling (ahh!), with only forty lanes back in Belgium and a few in Northern France, and four for the entire rest of the world. The Cadieux Cafe in Detroit has the only leagues that we are aware of. There's a brewpub in Minneapolis that got their start after visiting us a couple of years ago, who might have something in the way of a league, but I'm not sure. We've been doing our thing in Detroit since 1933!
A very sincere thank you to everyone who has chimed in!