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It loooks like upgrade successes are tied to half of your level. So if you have +24 you'll be able to upgrade from lv.48. And the best strategy here is to levelup earlier, don't skip any mobs and maybe even wait for some respawns so you can start getting upgrades faster.
I had a thought yesterday about using both saves and overlapping/alternating between them to rank up gear faster.
Save A: 1-10
Save B: 1-20
Save A: 11-30
Save B: 21-40
Save A: 31-50
Save B: 41-50
Got it finally but it took 7 loops. I'll use the above scheme for the next weapon, maybe it'll save a couple of runs.