OP, that sounds like one hell of a rifle. I love the 6.5x55 Swede. I have taken moose, black bears, elk, deer, wolves, coyotes and magpies with mine. The twist rate is a bit on the tight side for the bullets you list. I don't think you will have any problems as my rifle with identical twist rate shoots all of those well. The only drawback is that pressures build up quicker and limit your velocities to the low 2700fps range. Maybe even less.
Personally, I prefer the 140 grain bullets for any big game, including deer. Lots of folks prefer the 120-129 grain bullets.
I use 95 grain Vmax for coyotes/wolves and anything smaller.
All of the powders you list are fine for all of the bullets you list.
My go to powders for all of the bullet weights I use are H4831, Rel22 and IMR7828, All pretty much in the same quickness range to those you chose except for IMR 4350.
The performance you get out of your rifle will depend on how hot you load it. The loads listed for the 6,5x55 are kept low to be safe in the Swede M96/38 Mausers. Your Rem 700 and Lilja barrel should be able to easily handle much more pressure.
I started my rifle a Tikka T3 out with 260Rem loads.
For 140 grn bullets I use 46.0grains of H4831 over CCI250 primers. The Hornady SP Interlock, SST Interlock and Speer GS all like this load, don't show any pressure signs or loose primers and give very good case life. These bullets all group in the sub moa range.
For the Hornady 95 grain Vmax I load 47 grains of H414SL10 which is a kissing cousin of W760 over CCI 250 primers. This load gives me 3000+ fps. Sub .5 moa accuracy at all ranges.
Now, a lot of this accuracy can be blamed on the excellent quality of the T3. I have never seen one of them shoot poorly. All have been outstandingly consistent performers.
That rifle of yours should do every bit as well if it was put together properly.
Now that you have such a potentially accurate rifle and good loading components, you need a scope that is capable of wringing out the best accuracy the rifle can achieve. It doesn't have to have adjustable parallax but it should be of sufficient quality that parallax shouldn't be an issue, even on shots over 300yds.
Now all you have to do is shoot at incremental 50 meter targets and make up a chart for the butt of your rifle out to the longest range you feel comfortable shooting. If the scope you choose has multiple crosshairs on the reticle that will make life much easier for proper hold over at extended ranges. If the scope is good enough to have positive and repeatable adjustments you should be able to dial in for extended ranges.
You are also going to have to learn to dope the wind and mirage.
