I just pulled a couple of "FNB" manufactured 303 rounds and measured the projectiles, they were both .3125" and were Boat Tail. FNB are well known to have produced some of the highest quality 303 ammunition most of us have ever sent down range. I also measured a projectile from the also excellent Greek "HXP" round. It measured .311". Both of these rounds are very accurate in my BSA #1 Mk3.
If the 303 projectiles needed to be .316" diameter, one of the ammunition manufacturers in the past 136 years would have produced them with that diameter by now.
As for current needs...Cinchaga bullets (now in Ponoka Ab.) used to produce a 174gr flat base match type projectile at I believe .312" diameter. They were not cheap, in quality or price. Not sure if he's still producing or not but he has the dies.
Speaking of dies, since none of the mainstream manufacturers appear interested in producing a decent flat base projectile, consider this... if a few guy's got together and ordered a bullet making die set from Corbin that duplicates the profile of the mk7 round, you can use them to bump up .308 match bullets to the mk7 profile. I had an acquaintance that had such a set made to .3125" diameter, and they worked perfectly for that purpose. Hornady 178gr h.p. match bullets reformed very nicely, and the boat tail was removed in the process. The main issue is that corbin has about a year wait list, and they were around $1000 U.S. for the full die set about 10 years ago. The die set mentioned has since gone into the abyss after the owner passed away. Still, it's a viable option, as reforming existing projectiles takes much less time than initial production.