I solved the problem!
Using the clever utility, HwndSpy, I was able to determine that all of the instances where the font was not corresponding to what was expected (in this case, the default Windows font of MS Sans Serif), the font that was being used by the dialog was listed as "MS Shell Dlg". I searched the Internet and determined that Windows 98, while it seems to be advertized as using the registry to define MS Shell Dlg (as everything NT and later do) actually sets the value for this in the win.ini file! In looking at my win.ini, I saw that at some point that specification had been deleted (who knows when - I've had an issue like this for some time). So I added the line
[FontSubstitutes]
MS Shell Dlg=MS Sans Serif
and everthing is fixed! I hate the registry anyway, so I was glad to find the solution was with something as simple as win.ini! Hope this helps some other poor 98 fan.