German, one thing you might remember is the source of your 190 Sierras. There is a rumor around that bullets given to a Mid Tompkins or Earl Chronister were significantly more uniform than the general run. There is some real-world evidence for that (check with Steve Shelp), but it also could be just one of those shooting rumors perpetuated down the years. It makes sense to me, though -- if I were a manufacturer, I'd make sure the very best shooters, & people I used in advertising, got the very best I was capable of making. I see nothing wrong with that.
I have several lots of Sierra 190s from 1996 or so, and even within a box they show considerable variation. They shoot OK if you remember to sort them. With a 10-twist (likely in that rifle), I'd be more apt to try a 200, 210 or 220 Sierra, with the new Berger .308 Caliber 185 grain LRBT (Juggernaut) as a fall-back bullet. In the Sierra line, both the 200 and 210 are more modern designs than the 190s. A good lot of the 200s is a fine bullet indeed.
To the original poster. Whether or not the group will suffer from the 5 to 10 rounds due to heat, it is unlikely the rifle itself will be competitive. After all, that was not it's job. And if it were a Model 70 Match rifle, remember that highpower in the 1950s was not what it is today, never mind benchrest. If you're curious about what it will do, try it. If you're eager to win, build a rifle capable of that.
Edit:
In spite of the squawking you'll get from people, I've been known to shim scope bases .020. Better would be a high set of the Burris rings that use the inserts. You can get 20 MOA from them with absolutely no stress on the scope. Two +/- 10 MOA inserts come with the 30mm rings, but are now, I believe, an extra-cost option with the 1-inch rings. Cheaper than the semi-custom tapered bases. Amazon prices are about the same as Brownell dealer prices. I use them whenever making weight is not an issue.
