I have made a binary difference patch that updates the registered versions 1.0, 1.2b, and 1.2c to the latest version 1.2d. This latest version should have no digital sound issues. Because version 1.2d uses the DMA for sample playback, sound effects will sound much cleaner on the Sound Blaster 16 and AWE cards than with previous versions, which manually write each sample byte to the Sound Blaster DSP. The latest version is furthermore patched to correct sound effect dropouts on Sound Blaster 16/cards caused in part by speed-sensitive IRQ detection code.
Extract JILLUPD.ZIP into a directory that contains all three episodes, and run APPLYPAT.BAT in real DOS or within DOSBox. Version 1.0 did not seem to have the game selection menu yet, so I made a binary diff file that creates the menu executable from v1.0's JILL2.EXE. JILLUPD.ZIP also resets the high score table, and restores the deleted Commander Keen joke to Episode 1's map level, which is why MAP.JN1 and JILL?.CFG are overwritten. If someone provides me with other game versions, I can modify JILLUPD.ZIP so that these versions can be updated to v1.2d as well.
As I mentioned before, v1.2d of the game has one disadvantage: the music sounds worse because the .CMF playback routine changed (from an embedded late-version SBFMDRV to the Worx Toolkit's own routine). JILLFM.ZIP is the remedy: it redirects the calls made to the game's internal (bad) CMF player to Creative Labs's original SBFMDRV v1.22, which sounds much better in the drum channel. Extract JILLFM.ZIP into the directory after applying JILLUPD, and allow JILL.BAT to be overwritten. And if you don't like SBFMDRV.COM v1.22's playback, you can easily replace it with the driver version of your choice. In particular, you can replace it with the version that came with the Sound Blaster Pro 1 (2xOPL2) to hear the music in stereo when used with such a card, or with sbtype=sbpro1 in DOSBox.
Edit: Updated the two patches, new versions here.