Suzuki S40, good candidate for a turbo?
 

1- There's enough space to add a turbo.
2- At 8.5:1, the compression of the S40 is so low, it can easily get a turbo added on it, and not misfire.

I wonder also if increasing the compression ratio somehow, with thicker head pistons, will improve performance?

before you spend a grand or more on a turbo, swap in a stock cam from a 1990-1995 dr650. That may be enough power for you and its a lot cheaper.