You’re right with the tyres, the “choice” between two racing slicks and the Innova isn’t a choice, that’s just a pita. All I can do is to recommend switching to another rim size - to 349 mm.
If I, as a laymen, am able to lace my own 349er wheels I’d think that this can’t be a big problem for a professional wheelbuilder…but perhaps I’m wrong…
…Strida wheels are different from conventional wheels…omg… 
Well, I think there is still a small chance left over for the installing of gear drives,
BUT there are some major disadvantages and many details of course still unknown.
First; the installing would require a complete change of the drive train from belt to chain.
Next step would be to figure out how many teeth maximally are possible at the rear.
I know that 18 teeth fit, but I’d suspect - and wish - one could go higher, maybe up to 20T.
So - now one could start playing around at the front - possibly we could use here 56 or 58 teeth.
By using a chain there is also a certain chance of adjusting the chain line a bit left or right,
this may also help to get around the bottom tube.
Below a quick shot to illustrate on which base I drew my conclusions above; the parts to the right are a standard BCD 130 50 T chainwheel, laying on the original Strida 80 T beltwheel.
Left a standard pulley with 18 teeth, laying on a genuine 30 T belt pulley.
Interestingly, while writing this I contacted Wiktor from efneo, initially just for some drive details, got already several replies and therefore I’m sure they will help us - if possible.
Another interesting point is for my meaning the C1 bottom bracket:
Is it made completely out of carbon or is there an addidional metal tube inside?
If there is no metal I’d think once again about the project.
Finally a personal question:
The whole thing may end up with an overall gear ratio which is (let’s say) ten percent higher than normal - would you appreciate that or regret?