30-30 Winchester will work. Same rim thickness and diameter.
If you are checking in a Savage 99, you should put layout fluid on the locking surface at the back of the action, and mark where the top of the bolt rests with no cartridge in the rifle. Then check with the gauge and see if the bolt comes up all the way or not. It should on a go gauge, and should be short (lower than the mark) on a no-go. Keep in mind that the action may still look like it closed all the way on the no-go gauge, and you want the reference mark to see if the bolt fully seated. Wear and the springy nature of the lever/bolt connection make headspacing them a little tricky.
If it fully seats on both, well, you have a decision to make.
Is it a take-down model? Those are known for wearing loose and developing headspace issues, but a good gunsmith should be able to help you on that if you can find one who’ll work on it. If it’s not a takedown, I don’t think setting back the barrel and rechambering will help you. Wapiti1 is right, you will have a decision to make.
303 Savage is a cool gun with fun history. Basically big 190 gr cast bullets in a 30-30 case. But those 26” straight grip 99s are sweet guns.