As the OP said it’s been well used, I’d send it back. It will be disassembled to the frame, tossed in the solvent tank and completely rebuilt. You will get the press back in brand new condition. From that point, anything that breaks from normal use will be replaced via warranty.
I can understand Dillon’s perspective in this situation. They have no idea what’s going on with the press and would be relying on the end user (who is admittedly new to reloading) to properly diagnose and correct issues. This can very easily turn into a cascading parts problem, which they have very likely been through this many times in the past. The service fee is very reasonable considering what you’ll receive in return. I wouldn’t try to take undue advantage of a generous warrantee policy. I’d let them restore it and from that point they will supply their complete warrantee service for the rest of the time you own the press.