There are certain issues involved when barreling a modern, push feed bolt action to a rimmed cartridge. Primary among them is the extractor. Also, recessed bolt faces make it difficult, if not impossible, to headspace on the rim as the cartridge design intends.
Actions which feature non-rotating extractors work best. Examples of this would include such actions as the Ruger77, the Winchester M70, the Mauser, and, naturally, the P14.
The Savage could be utilized in one of two ways.
The first way would be to mill away most of the bolt recess, leaving only what would be necessary to hold the extractor. This would allow for about 60% of the circumference of the breech to be left to support the rim. This would work out OK.
Method two would entail the fabrication of a non-rotating extractor which would be attached to the gas baffle. It might be as easy to simply make up a new baffle which incorporates the extractor.
The Reminton 700 would also require significant modification in order to chamber it for the 303. Once again, modification of the bolt nose would be necessary in order to headspace on the rim. The use of a Sako extractor would allow an easily done modification. To forestall the hue and cry from those who have declared the Sako extractor conversion unsafe, let me say, the sako extractor in this mod is probably as well contained as that on a lee enfield. If safety is truly a concern though, one could use the Sako style baffle on the modified Remington bolt.
The M70 or the MRC1999 or the Ruger 77 could all be fairly easily done.
Feeding from any of these is quite another matter and wouldn't be all that easy to address. Maybe an easy way would be to set the rifle up to use a Lee Enfield magazine. Otherwise it is necessary to install an angled spacer, front and rear, in the magazine box. This makes it necessary to use a long action in order to have enough room in the box for the spacer. Regards, Bill.