The gun is a treasure. Please continue to care for it well.
Scopes. This cartridge is in the .30/30 class. I wouldn't get to excited looking for a scope much over 4x. Many of the old, low power variables had straight front. They didn't need to collect all that much light for the low power lens system. You can mount lower and have a more handy rifle. But you have to be happy. Hit the web sites and look at the options. Many less expensive that should stand up to .30/30 cartridge and get the job done. Midway.com. Grafs.com, Wideners.com, MIdsouthshooterssupply.com, etc.
It kinda sounds like it is the age of your cases that makes for the necks cracking. One batch of surplus military was sold with cracked necks. Seems the necks were not annealed just right for that brass. I would try some new brass (yes, a bit difficult for the .303 Savage) before making this a final conclusion.
You can anneal necks. The easiest way, melt pure lead, muzzled loader balls if necessary, and take the UNPRIMED CASE by your fingers, and dip the neck into the liquid lead for the area of the neck you want annealled. When it is too hot to handle, drop into water, bucket, whatever... Luck.