Even if working the Savage bolt is like shoving a stick into a can of small rocks.
I can certainly help you love your Savage action again.
Check the bedding as this sounds like there is a bit of bending going on. An action with a well used bolt should just glide back and forth under its own weight just like a custom. Try loosening the rear bolt and see if the bolt travel smooths up. Take the action out of the stock and see if this smooths things up.
bolt timing is a big improvement on the ease and feeling of cycling the bolt. some factory actions are seriously clunky
the 338 RUM = the 338 Lapua at standard magnum pressures. yes, you can hot rod the Lapua but that is most certainly way over SAAMI spec. 300gr rated at 2700ish FPS.
the 338 edge is a 338-300RUM with no shoulder changes. Typical gain of 100 to 200fps over the smaller RUM/Lapua with 300gr. 2800 to 2900fps
the 338 LM improved is similar to the Edge in case capacity so will do the same thing
338 tomahawk or Mystic - 338-300RUM Improved and throated long. In long barrels you are around 3000/3100fps. Standard length barrels a solid 2900+fps
Variations on barrel lengths and quirks can have all these larger cases overlap in accurate velocity.
The real boomers start with the 338-378 Wby. Getting more juice with the 338-416 rigby improved and ending with the 338-408chey Tac.
Each step gains you another 100ish FPS and the CT monster is supposed to spit the 300gr MKs OVER 3300fps in a 28" barrel.
The cost to build on a Savage action is equal in any chambering. A 338 Edge barrel is no more expensive then a 223.
All the extra costs associated with a Rem build simply aren't there.
In fact, for hunting, the Accutrigger is one of my favorite triggers and it comes for 'free'. Around 2lbs with no creep and overtravel. My present VLP is under 2lbs with factory parts.
There is little reason why you can't build a semi custom Savage for around $1000.
Jerry