"a specialist advisory company helping clients deal with Oracle licenses" I would (naively, I know) imagine that if you need to hire a third party to help you sort out your licenses with a vendor, you would do whatever it takes to get rid of that vendor. It's almost as if Oracle wants their customers to ditch them the first chance they get.
Once you're using an Oracle database, you are probably using proprietary Oracle features, SQL syntax, client libraries, etc. The first chance you get might be a while. I once worked on a project porting an app from Oracle to another commercial DB. When Oracle is deeply embedded in your applications, it's easier said than done.
All our business logic was into PL/SQL stored procedures, I migrated them to MySQL stored procedures.
The MySQL language is a bit retarded, and some extra work was needed, but everything was doable.