I can't find exactly what this Tawny-OWL thing is (his link is broken), but it sounds like it might have some kind of interpreter application provided. If he is offering a finished application within the same build unit as his UI library, this is the "big ball of mud" architecture. The fix is to break his application out into a separate build unit that depends on his library. The application can then include slf4j-nop without messing up SLF4J for all his library's consumers. Maven Reactor can automatically build his dependencies when his main application builds, if desired.
The thing about having to deal with 2 different logging frameworks is exactly what SLF4J is meant to fix. SLF4J lets you route the messages from multiple sources to a single sink/backend defined by the final consumer application. Yeah, it sucks to deal with multiple logging frameworks, but that's simply how it is and you don't help anything by having a whinge about it. You include the routing/bridge modules (JUL-to-SLF4J, Commons-to-SLF4J, etc) in the final-consumer application and call it a day. If you don't want to do that, find some other dependency that doesn't use those logger frameworks.