No issue using the RUM 700 as a donor for a .338 Edge or 338RUM ... Just add money for a full blueprint of the action. true, lap lugs re thread and the list goes on.
It also depend if you want to mag feed it ... extended mag box MBE3 Wyatts. retime bolt, etc. You dont want to have to seat the 300gn pills too deep.
Depends what your budget is and if the 300RUM barrel is cactus?
New tactical stock and the list never ends! Trigger..(once you have a Jewell its hard going back)
Sometimes you may be better off getting say a Stiller TAC predator type action. Then if going this way the Lapua is a worthy option.
Re Lapua, I'm not agunsmith but mine wont build a Lapua on R 700 action. Its a lot fatter so the bolt face doesnt really match. The factory Remmies in 338 Lapua are also a bit hit and miss and pretty thin in places.
I forgot to add you will need custom dies for an Edge which is no biggie really .
Go to the Defensive Edge web site there is a lot of info on the 338 Edge there by Shawn Carlock. I got my dies and other bits from him.
If you are shooting a lot, you may want to consider the price of brass for a Lapua but its really good and lasts a while. Remmy brass is fine if prepped properly
If you want to use your existng action find a local recommended smith with an Edge reamer and wait for him to build you one. Its just not as simple as screwing a new barrel on if its accuracy and LR shooting you want to do.
Once your bitten by the bug the quest for accuracy never really ends! The distances get bigger as well.
My next one build is a custom 7mm Dakota on a Lawton action..ABS barrel
Mind you I still have a 700P in 7mm as the wait for a custom rifle
can be a darn long time!
Honestly you are lucky in the US,,, Just buy one of the rifles on this site from Len it will save you waiting and take a bit of the headache out of it.. I wish I could without Tax and import duties and loads of paperwork! In the end you wont be far off the mark cost wise.