I finally encountered some knowledgeable inmates over on Adventure Rider. Let me amend that because there are a lot of knowledgeable inmates there. I'm referring specifically to inmates that have experience with the NX. I retrospect, it seems that I might have an air leak, someplace, between the carburetor and the cylinder head.
Normally, the sure sign of an air leak is a slow but steady rise in rpm as the engine warms. Usually a shot of carburetor cleaner or starting fluid on the intake manifold will cause the rpm to increase dramatically (these are flammable fluids, you see). I've never tried this method to try to diagnose the issue because I've never suspected an air leak. The NX is twice as susceptible because it has two o-ring seals; one between the carburetor and the intake and the other between the intake and the cylinder head. What makes it more difficult is that the air leak, minor as it may be, would seal as the parts warmed (expanded). This pretty much explains why the issue was more prevalent when temperatures were cold (20º-50º F). Another clue would have been that the float bowl sealing gasket recently quit sealing. These are the parts, o-rings and sealing gaskets, that suffer the most from age. While mechanical components fair pretty well, these parts still tend to degrade even though they still look good and feel pliable.
So, I ordered a carburetor gasket set (which includes the carb-to-intake o-ring as well as the float bowl gasket) and the intake-to-cylinder head o-ring. If there is an air leak, however slight, this should seal it and resolve the leaking float bowl, too. I would still like to check the valve clearances as well as the compression. I ordered from Honda Parts House in Muskegon, Michigan. They seem have the best OE Honda prices I've found on the 'net and are relatively close to me (Chicago).