RE: Looking for a bigger gun
It is probably difficult to improve on the -06 with simply an Ultra-30, unless you routinely make 350-400+ yard shots. (There are already the High Energy/Light Mag loads for the -06 which knock on .300 WinMag/WSM performance levels) In a similar situation, I'd probably just jump to a .338 WinMag as a primary elk gun, or maybe even down to the .270 for strictly white-tails / mulies. You appear to have already chosen a chambering which could cover 100% of lower-48 big game needs...
But good luck whichever way you choose!