Thanks to a message from a member here who tipped me onto an idea, I have found the cause of this problem and have resolved it. The problem wasn't the length, but the true problem was obfuscated by the fact that when I thought I fixed the problem (pulling the bullets and resizing the cases to try a new length), I fixed the REAL problem which was the fact that the cases were not sized enough.
It seems that the Savage has a really snug chamber on it compared to other guns. The brass I resized once would still sometimes be quite snug and sometimes stick trying to load or eject. I've found now that if I run the same case through the resizer with a few extra full rams (2-3 pulls now instead of one, and on the first pull, I pump the lever a bit to really size the lower part of the case, which I suspect is where the jamming might be happening.
Anyway, I just did case prep on 50 cases last night using this sizing method and every single test case has chambered and ejected without effort.