I recently got a PM asking for an update, so I'll go ahead and post one now. Basically, things kind of worked themselves out. He did wind up going with me to work out, and we both hit the showers when we were done. Like I said, they're open showers, so I saw him again and he finally saw me. We stood next to each other, and I caught him looking at me several times. It didn't matter to me, because at least this was a public non-sexual situation to be naked. (Thanks again to whoever suggested the gym and shower idea. Good call.) He didn't say anything while we were naked, but he commented about my girth when I was driving him home. (I have to admit, I think he's an inch or so longer than me flaccid. But I'm definitely thicker.) We talked about length vs. girth, age and growth, etc for a while, and then we moved on. It was strangely anticlimactic.
Looking back on the day I brought the TV over, I'm pretty sure that's what this whole thing was about. He has no dad, no brothers, and I think maybe a couple male cousins that he never sees. He also said none of the guys at his school use the showers, and his guy friends think it's "gay" if another guy sees you naked. This is a kid who has practically never seen another dick in person. So it makes sense that he would do some weird shit to try to figure out if he's normal or answer whatever questions were in his head regarding his body.
He wants to keep working out with me, so we're planning to go together a couple times a week. Of course we'll still shower and stuff. But I don't really think it's about dicks or nudity anymore. I think it's just a time to hang out and talk a little bit about whatever. Body issues are definitely one issue, but I think he may have some confusion about his sexuality, among other things. And that's fine. Now that we're more comfortable with each other, I'll just wait for him to guide our discussions and talk to me about stuff when he's ready. It's been for good for me to do something other than worry about myself, and I'd like to think this will be good for him too.
Anyway, thanks for everyone's advice. I think this might be the first time I've had success with advice from an internet forum. So that's cool.