I know of one that was built with a Lyc O-235. After the builders put it on scales, and calculated the C.G. position, he ended up removing the engine, selling it, and installed a Rotax.
I believe there is one other one actually flying with a Lyc O-235 (I think in Arizona?). I do not know what that builder did to correct the weight / balance issue.
Most likely, any type of Lyc/Cont will be much too heavy. Take a look at the nose structure of the RV-12 and you'll immediately see why! It was designed for 165 lbs, not 200+.
If you want a nice Rotax alternative, check out Jabiru.
You can check "Paul Lefevers RV 12" out on You Tube theres a video clip of his aircraft..the Rego is N198PR
Hope this Helps Cannot get any info on it though!
Cheers.