Is it realistic to assume that a 3rd party application that can be customized to work with my database model can't be customized to work with a model exposed in some other way (web service, J2E, .Net or whatever)?
No, it isn't. Database interfaces are very simple, text and table based, have been used for many years, are well tested, work reasonably well and fast, there are tools, bindings for every language in existence, and thousands of trained programmers. To change them for web services (I don't know how .NET or J2EE are equivalent) is not realistic at all.
