There needs to be an understanding or "Why they don't work?" before "how do I make them work?" The topic of Slugging a barrel would be a better comment in this instance, along with an understanding of what is safe and what is not.
Ok...
I happen to have one of those 303 barrels and have slugged it. The land diameter is 0.303", the grove diameter is 0.316". The groves measure 0.098" high. It's hard to see those features on the slug in a photo, so here is what it looks like drawn out in CAD:
This gives you a cross-sectional bore area of 0.0734". The default cross sectional-bore area in Quickload for a .308 barrel is 0.0736". So, my Enfield barrel is tighter than a typical 308 barrel (and likely rougher). The .303 British cartridge has a capacity of about 56 gr. H2O, the same as the 308 Win.
SAAMI pressures:
.303 British -> 49,000 psi
.308 Winchester -> 62,000 psi
The tightness of the 2 groove barrel along with the relative weakness of the Enfield action is know about and considered in load data for 303 British. Using it doesn't blow up the Enfield. Using .308 Win data for the same weight of bullet in it likely would. Logically, would using the .303 British loading data for that bullet in a larger .308 barrel, in a case that has the same capacity, produce a higher pressure than it does in the 2 groove .303 barrel? It shouldn't if the other clearances are adequate. Where there could be big problems is if the larger bullet diameter creates a situation where the neck is too tight to release the bullet (same danger as a tight neck chamber).
The reason those adapters don't blow up guns is because 7.63x39 is only rated for 45,000 psi. and a lot of the bores on those com-bloc rifles were just as tight as this Enfield when they were new (those countries weren't know for holding tight tolerances). It's considered in the SAMII spec. for the cartridge. Which is why firing the rounds in those adapters doesn't produce anything close to 308 max. pressures.
Yes, it's advanced stuff, and no a beginner shouldn't be attempting it. Is it any more dangerous that wildcatting? No, it isn't, and many aspects of that also violate the warning section of your loading manual. Saying that it will automatically blow up a gun is false, it's akin to raising warning flags when someone asks about blowing out the shoulder of a case, which is also usually what happens when you explain the process of creating an Ackley case to some who "has reloaded for 40 year", but has never done anything outside of following the recipes in his manuals. "Good God! You're firing a cartridge in a chamber that doesn't match it, everyone knows that'll blow up your gun!".
Doing something like this when you don't fully understand it
IS dumb, but so is waiving your hands in panic mode when also don't really understand it either. I'm not going to tell someone to go out and do this, nor would I tell them to go ahead and wildcat a completely new cartridge or build their own 50 BMG from scratch. People have done these things and I'm not going to start preaching to them from the intro section of a reloading manual if they insist on doing them. They ultimately assume the the risks. And the risks are much higher when you start playing with an over-sized bullet, just as they are when you start creating loads for a completely new cartridge or build a big bore rifle from scratch. Hopefully, the person has the good sense to run the initial tests in an isolated area, hiding behind cover and pulling the trigger with long piece of string (with the understanding that they may lose the rifle). If they don't, they're a moron.