Is there any way to fix this without repainting?

Nope. You're down to the base coat, and that has a dull finish. You should be able to sand it to a feather edge, then add a new coat of clear coat. It should blend in with the clear coat still on there.

I would enlist the help of the people at a smaller body shop. Ask if you can mask the adjacent panels, then stop in when they're going to be spraying a customer's car. They will have extra clear coat mixed and will just put it all on the car, . . . unless they can throw a little of the extra onto your car. If they spray it on your car in the parking lot, they might be happy with a small tip or box of donuts. They won't be responsible if dirt gets blown up into it. If they're willing to do it for you, consider bringing along a large piece of cardboard to set on the ground to stop the dirt from flying around.

You also might check for an Auto Body program at a nearby community college. They'll want to use your car for a valid learning experience, but they might be willing to spray the clear coat without doing the sanding.