I converted one Garand to 308 Win, needed to install the magazine spacer to reduce brass shavings in the magazines.
I have one pre 64 M70 that would not feed 308 Win reliably until I purchased the short magazine conversion parts. My pre 64 was originally a 30-06 NM action, fed 30-06 fine, but 308 Win rounds slid around in the magazine and wound not feed correctly. Your rifle may or not feed reliably with a short round in the magazine. I would leave any M1903 with 30-06 length cartridges. Such as , 270Win, 35 Whelen.
I did convert a CZ Mauser, originally in 7mm, to 308 Win. It is finicky about cartridge stacking.
I owned a National Ordnance M1903A3. Did not shoot it much. Extracting a round became more difficult, and it was due the receiver seats peening. The bolt lugs were in a hole, and opening the bolt required getting those lugs out of the hole, and compressing the fired case. In time, the case head would have blown, and this would have happened to me.
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I would not fire any National Ordnance with anything. The best thing to do, is to remove the GI barrel, bolt, and other GI parts, and scrap the receiver. It is not worth getting hurt experimenting to determine the minimum load required to burst a case head.