With a 38t small ring, you can use a "normal" 130bcd... most people using compacts do so because they want a smaller front ring than 38. That said, there are 36 and 38 tooth rings available, for example
these FSA Pro Road.
I did notice, however, that Shimano doesn't offer 36t rings for its 110bcd cranksets. You may have the compatibility issue that you are worried about. I'm guessing that you'll be ok though, with a 36t ring as long as the der. doesn't contact it. I think you'll also find reasonable shifting performance. Any special ramping and pinning optimized for 50-34could be counteracted by the reduced jump in ring size.