Well, to wrap up this thread:
Like a total idiot, after cleaning the carb the first time, while hooking up the fuel hoses I installed the old inline fuel filter (that I had added) backward. So all the junk that the filter had trapped was flushed into the carburetor. So, I got to clean it again.
I also discovered the carb was leaking gas into the engine because the hole in the brass seat for the float needle had become enlarged, so the needle's rubber tip wouldn't seal. Ordered a repair kit for 20-something dollars, replaced the seat, put everything back together ... and the engine wouldn't even turn over.
Removed the spark plug, cranked the starter, the engine turned over and the gasoline that had leaked from the carb into the cylinder was forcefully expelled thru the spark plug hole (a good thing).
Replaced spark plug, hit the starter, and while the engine happily turned over, it still wouldn't start.
Sprayed a shot of starting fluid into the carb intake and the engine fired right up, for about two seconds until the fluid burned off, so I knew I had compression and spark. Therefore ... no fuel.
Took apart the carb again and discovered that the main jet, which is mounted on the side of the fuel riser in my carb, was clogged. I hadn't even known it was the jet until I found some more documentation online -- I thought it was just a little bolt.
Cleaned it out, reassembled the carb, reinstalled it ... and the engine still wouldn't start.
Then realized I'd forgotten to plug in the electrical connector for the fuel shutoff at the base of the carb. Plugged it in, cranked for a while, and the engine finally started ... for the first time in months.
I still need to adjust the valves, but at least I now have the damn thing running.
Thanks for the helpful suggestions from others. I'm sure I'll be back again.