Well, as you mentioned; this is a known limitation -> Cannot participate in distributed transactions; they support single-site transactions only..
Postgresql has a feature/concept called "Foreign Data Wrapper". Foreign Data Wrapper for Oracle. So you may have a look at that.. For integrating Oracle and PostgreSQL that concept can be used as well.. It is like create a link from postgres to Oracle.. But I didn't test it, you should check its limitations.
As for publishing web services from Oracle database, you have option . But first you should decide with your developer that it can be done aligned with your transactional logic.. I mean you should decide whether it will work in your scenario or not.. You should also decide the type of web service that you should publish. (rest json, rest xml, soat etc..)
Some examples with ORDS :
https://www.oracle.com/webfolder/technetwork/tutorials/obe/db/ords/r30/Insert_Update_Delete/Insert_Update_Delete.html