Same here; my solution was just to let the strings go dead and it works. Aside from some tuning stability problems on the octave strings (which has more to do with my right hand than anything- I beat the SHIT outta my basses.) The bass strings are still fine. I have been considering extra-long scale guitar flatwounds for the on pair of the octaves but I don't play it enough to justify the hassle right now. I'm getting ready to start playing out again and I think my TP12 could prove very useful in filling out a power trio.
I hate it when the strings are dead on a 12-string. I use a stereo system with the neck pickup going clean and bridge going through Rotosphere II which adds a bit distortion and Leslie effect when needed. Sounds big and not muddy at all even if I plug into one amp (Hiwatt DR103, clean into Normal ch and dirty into Bright ch) which I do most of the time.
My band is a trio of two guitars and bass (plus drums occasionally) and I use the 12-string for about 50-70% of the stuff we do live so I admit I wouldn't have made the effort if I just used it occasionally. When we started I used the 12-string all the time and I use the same stereo setup when I switch to a 4-string.