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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!

I'd look into the 7mm Rem. Mag.
The ballistics on that round are very impressive.
I've had mine for almost 2 years and it's the only rifle I have that I feel confident with when it comes to long shots or tricky shots in cover.

I use the 300ultramag for elk and moose due to it's flat trajectory and high energy at longer distances.It works great but recoil is much harsher than the 30-06 or 7mm rem mag.For deer I use the 7mm stw as the power of the 300ultramag is not required.Most people will find the milder recoil of the 7mm rem mag or 300 win mag more to their liking and if you don't shoot long distances as in the 400 yard range or further the ultramags offer no real advantage over the standard magnums.