Ah - my apologies... Lead CORE bullets, not lead bullets... I have the luxury of not living in a communist country, so I'm not forced to live by misguided and irrational law, so when someone says "lead bullets" to me, I don't assume that they meant "lead core, copper jacketed bullets". I assume they mean what they say - lead bullets...
Based on your last post, I'm not sure you're understanding what Bassman and I are saying:
You can't go longer than 3.40" in your action. Your RIFLE is the limiting factor. The last line in your last post indicates that you're missing this point - there is no cartridge that "will allow a longer COAL" in your Ruger M77 Mark II, the RIFLE will not allow a longer cartridge unless you remove the ejector and convert it to a single shot.
As such, your only "faster" options for 3.4" compatible cartridges are 7mm-300 and 7mm Dakota, which aren't going to be fast enough to make a difference. If you really do have a velocity vs. twist rate problem, then neither of these will gain enough speed over the 7mm RM to make a 9.25" twist work.
Since my first name is Dakota, I built a 700 in 7 Dakota, the gains there are minimal - and based on the data from CEB, you'll need a fast twist barrel anyway, so the end solution is the same - a faster twist barrel - but you'll spend 2-3x more on brass and more on dies, with no real benefit.
Personally, I'd throat out that 7mm to accept long seated bullets to fit your maximum mag box - matching it up to the CEB bullet weight you want to shoot, and work on my seating depth.
I've shot a lot of all copper bullets over the years, CEB's included. They don't follow the same rules for ideal COAL as conventional lead core bullets, and I've seen a lot of reloaders make the same mistake that I made on my first foray into copper solids - you don't seat them the same as lead cores, they like a little room.
Your twist rate is likely the issue - and you won't be able to speed up enough to fix it. Even with a RUM case, you won't get enough speed gain. The CEB site suggests a 1:7.5" "or faster" twist for their 180 and 195grn MTAC and MTH. I'm not sure it'd need to be that fast in a 7mmRM case, but a 9.25" standard twist won't cut it. I'm calculating an 8-8.5" twist for these bullets.
However, in running the numbers, you'd have to get over 3600fps for a 1:9" to stabilize these bullets - which the RUM, STW, Dakota, and others just won't do.
So I'd either pick a different bullet, different bullet weight, or strap on a faster twist barrel in the same 7mm RM. All of your other cartridge options will either have the same problem with twist rate, or won't fit in the rifle action.