I tried a ton of different things with varying degrees of success. The trial and error (mostly error) part was actually quite fun at times.
I have tried, and you might consider, the following:
* augmenting with hand percussion or manually add additional fills with the drum machine (as noted above).
* run the drum machine through an amp, and mic the cab much like you would a guitar.
* experiment with distortion...I've used guitar pedals and sims for this in the past.
* anything else you can think of.
All of my efforts resulted in somewhat lo-fi, arguably quirky drum tracks, but I found at least some to be pleasing.
At some point I did decide to just let it sound like a drum machine, and make my arrangements blend with that sound rather than trying to mask it.