I have been doing exactly what you ask about - new 8x57 PPU brass formed into 9.3x57 brass - simply run the original 8x57 (.321 ID?) into Hornady Custom 9.3x57 die with a long tapered expander like in several Lee dies - maybe all Hornady expanders made that way?? Result is what appears to be 9.3x57 cases - so perhaps .364" ID?? As recommended on-line - from that 9.3x57 die sizing, I then go on, by using a Lyman die for 41 mag (perhaps .408" ID?) - so makes into a nearly straight wall case - then back into that 9.3x57 die to set the shoulder so that it is just snug to close the bolt on my rifle, who's Husqvarna barrel is apparently chambered for 9.3x57. Then fire-form. I do not own 9.3x57 gauges, but that brass then fits to that chamber - whether it is to 9.3x57 spec or not, I do not know (nor care!). Perhaps not as quite drastic as OP wants to try - perhaps an annealing step, besides lube, might be appropriate?
Is several posters on CGN - myself included - who have used the COW method to "blow out" 300 Win Mag and 7mm Rem Mag brass into 458 Win Mag cases.