To directly answer you - no, I never tried that. What I would do - is load one up see if that dummy round can be chambered - that bullet might make the neck too fat for the neck area of your chamber. If it fits okay, then I would work up a load for blasting away - not likely that you will get very close to your lands - I suspect is perhaps a very short bullet - but being a wad cutter, maybe the ogive diameter is close to the front end?? A new-to-me one that I am playing with to reload is a 7.62x39 - with 123 grain jacketed bullets - is not much for "seating depth" - much, much less than I am used to in other cartridges - might be what you run into? Is a lot of concern about a few thousandths sizing different than the bore size - but I would be more concerned about the "throat area" fill - the lead bullet will swage down to whatever that bore wants to see, I think, if that bullet fits into the throat. All within reason, of course - if you say the bullets are .313" - there are/were some 303 British rifles with as much as .316" groove size or more - and some as small as .310" or less. Is all about how much powder - how much pressure that you create with your hand load - is a good section in Richard Lee "Modern Loading - Second Edition" about matching breech pressure to cast bullet "hardness" - at least Richard Lee's thoughts about it anyways - others may disagree with him.
Further - again, I never did so on purpose - but read many times to get ALL copper jacket residue out of the bore, before trying to shoot cast lead bullets - they apparently do NOT get along - you apparently will not get good results shooting cast bullets in a barrel with copper jacket fouling. I just do not know about the cupro-nickel jacketing that was apparently common in elder milsurp ammo - and I have heard it is a real "bear" to get that stuff out of a rifled bore, to be clean to bare steel. As bizarre as it may sound, someone could have fired off a box or two of milsurp cupro-nickel in 1922 - and if never properly cleaned out - that jacket fouling is still in that SMLE bore - more than 100 years later.