I'm mounting some fenders on a bike that doesn't have an integrated derailleur hanger in the rear horizontal dropout. Rather, it has a typical claw plate. This takes up a lot of the dropout, and it would really help in getting better fender clearance if I could get the wheel a little further back in the dropout. The current setup is already all the way to the back, and it doesn't look like there is much room for grinding a little more clearance into the plate.

So I'm wondering are there any other solutions that people have done to get a little more room in the dropouts? I don't need much, we're talking millimeters.

That's a tough one. How about a narrower tire?

Neal

They have lots of different ones here:
https://derailleurhanger.com/
Maybe something would work?

The traditional horizontal adapter-claw hangers usually had a nut and bolt to hold the claw in the dropout and to precvent it from simply rotating. If you are handy with a high speed drill you might remove the fixing screw entirely and then just slide the adapter all the way back and tap both the hanger and dropout for a couple small machine screws to attach the adapter. This is basically what they use on modern aluminum and carbon fiber bikes - which almost always have replaceable hangers.