Doing the obvious and checking CPAN, there's Statistics::R and R::YapRI (have had people at $work use the former with some degree of success, just saw the other so YMMV . . .). I believe those however are more intended for letting you call into R from perl which sounds maybe the converse of what you're trying to do.
As far as your suggestion of turning the perl bits into a REST/web service that's probably as good a solution as any (and Mojolicious as good a framework as any). That'll let you make a clear break with a defined API and has the added benefit you then could have clients in ANY language call things (say let the python using heathens in on the fun too).
The cake is a lie.
The cake is a lie.
The cake is a lie.