I had a similar problem several years ago. I had a dll written in Delphi. (Delphi was a Pascal-based Windows app development tool sold by Borland.) I needed to call the dll from Java, but some of the dll functionss had parameters and return types that that were incompatible with Java. (As an interesting, if irrelevant, aside, Anders Hejlsberg, who invented C# for Microsoft, also invented Delphi for Borland.) Here is how I solved the problem.
1) I did use jni to allow my Java code to call a dll.
2) I wrote a thin wrapper dll in Delphi that was the actual dll called by my Java jni code. For those functions that were completely compatible with Java, the wrapper dll simply acted as a pass though, directly calling the actual dll functions and returning the return value. For those functions that were not compatible, the wrapper dll defined corresponding methods that were compatible with Java and did the appropriate translation from Java to Delphi before calling the actual dll.
3) I also wrote a thin wrapper object above my jni calls. Again, for the most part, the java wrapper directly made jni calls for those functions that were completely compatible between Java and Delphi. However, in my case, a few functions required that I pass in Delphi objects. So, what I did was define corresponding Java objects. The main purpose of my Java wrapper object was to take these Java objects, translate them into parameters that were compatible with my Delphi wrapper dll, and then make the apprropriate jni call. Also, for those dll functions which passed back an object, my java wrapper took the java-compatible return value from the jni call, and created and asssembled the appropriate object.
This may sound like a lot of work, but it really was not (and my dll had over 100 methods, and a dozen or so Delphi object types). When I was done, writing the Java application code that actually used the dll was very straight forward.
Regarding the generics, that could be a problem. But, if in real life, the number of object types you support is relatively small (and it often is), you can just write separate calls for each object type in your wrapper. (That is what those of us who remember Java 2 used to do before they invented generics and it worked just fine, even if it was a bit less elegant.) Your application Java code could stll use generics; the wrapper would make the appropriate call based on the actual type that was passed in.
Hopefully this will give you some ideas on how you might proceed.