jjaf's comments prompted me to try a few experiments. I haven't 'solved' the problem but I have some observations. Others may have useful comments or suggestions that I can take into account before I do a lot of retagging, try another server, etc.
As far as I can tell, the problem involves multiple disc sets. I've used the discnumber tag to numerically tag the files corresponding to each disc.
For example, I've ripped an 8-CD set of Bach orchestral works, yielding 147 mp3 files. I've tagged all 147 files with the same Artist, Album, Genre and Composer tags. The 15 files ripped from CD1 are all tagged with discnumber 1 and those files are consecutively tagged with track numbers 01/15, 02/15, etc.; the 20 files ripped from CD2 are all tagged with discnumber 2 and those files are consecutively tagged with track numbers 01/20, 02/20, etc. And so on for all 8 CDs.
Note that there is only 1 Album (not 8) because all 147 files have the same Album tag. I thought that this would let me play all 8 discs by selecting a single album on my Roku. However, WMP apparently does not process the discnumber tag correctly (or at all). I wind up with track 1 of all 8 discs (i.e. 8 tracks in total, ordered alphabetically by Title), followed by track 2 of all 8 discs (i.e. another 8 tracks in total, ordered alphabetically by Title), etc. This is not very appealing.
A brute force solution would be to change the Album tags by adding "disc 1" to the Album tag for all of the files belonging to disc 1, adding "disc 2" to the Album tag for all of the files belonging to disc 2, etc. But, if I do that, I won't be able to select the whole 8CD set as one album; I'll have to select each album separately.
Another brute force solution might be to create a playlist and somehow arrange the correct track ordering within the playlist. I'm not sure if that's possible though (I haven't fiddled with playlists yet) and in any case it seems like a lot of work.
Another solution might be to try another server such as Firefly, but before I do that I'd like to know if Firefly pays attention to the discnumber tag such that the foregoing problem would be eliminated.
I appreciate the input everyone has offered so far and I'd welcome further comments or suggestions.