If you don't mind this is my opinion on the subject.
If you can do the work yourself or have someone you trust that can do the work then re-barreling to 7x57 would be the best option.
If you do not have the ability to do the work yourself then leaving it in 7.65x53 becomes the best option.
Its hard for me to recommend someone paying $300- $400 dollars to get the gun re-barreled.
Please understand that the old barrel has been on the receiver for over 100 years and its possible to crack the receiver removing the barrel. It doesn't happen often but a lot of people would take an old receiver and cut the barrel with a lathe. Doing that ruins the old barrel in some cases. but its better than ruining a receiver.