So, to bring this thread to a close, convinced that I needed a different horn, I went to a local hobby store (that I didn't know was in a relatively nearby town) and talked to one of the kids there. I came away with another 25T horn. It looked kind of small, but at least I wasn't having to wait for something to be shipped.
Well, the new one was the right length, but not height. It fit the servo gear perfectly, but didn't have clearance over the servo body for the connecting rod to fit. But in thinking about my talking with the kid, I decided to maybe work a little more with the Spektrum 25T horn I mentioned ordering earlier in this thread. In my earlier attempts to get it to fit, I think I kind of mangled the outer edges of the threads, but as I placed it on the servo gear, I could still feel it "click" into place. So, I was able to hold it still, and screw it down (I did use Loctite) far enough to where it made good contact with the servo gear. It didn't seem to cover as much of the gear as the one I'd just bought, but it worked and most importantly, the connecting rod fit.
So, I'm up and running with my first build. As I've mentioned, I know it's not the hottest setup on this forum by any stretch, but I really enjoyed the process. I'm sure upgrades are coming in the future. That said, I now fully appreciate just how fast these things are. I don't have a ton of space at our house, so I'll need to take it somewhere more open for some real wide-open throttle experiments, but I've just got it on a 3S battery right now and when I put the transmitter at 100%, it really takes off. I can only do full throttle for 1-2 seconds in our area. I'm mostly keeping it at 50% for now and doing doughnuts in the gravel/crusher run below our house. It's a lot of fun and our two beagles have had a blast chasing it around the yard. The R/C is fairly heavy so I'm careful to not actually hit them, but when I am ahead of them, I open it up a bit to let them run.
Thanks for everyone's guidance!