The RUM, Lapua & Edge are all within 50-100FPS of each other. Not exactly a deal breaker. Most feel the Rem 700 action is a little on the small side to run the Lapua but heck, they started chambering factory rifles in Lapua last year
The RUM & Edge will be the cheapest to reload for, brass wise. The one fact that will usually be over looked is brass life, if your brass is 1/3 the cost yet has to be replaced 3x a fast, you really aren't gaining any ground. I love my RUM, don't get me wrong. It'll hang with the Lapua velocity wise, any day of the week, at the the cost of my brass (3x-4x reloads before they're toast, usually).
Shawn Carlock (of Edge fame) has the ability to acquire Lapua "quality" brass for the Edge, effectively increasing the appeal of that particular cartridge. The Lapua has long been the .338 mag gold standard, nuff said
. The RUM has had brass availability issues in the past... The RUM also has the shortest powder column, allowing the end user to seat the bullets out farther while still feeding through a magazine system.
When I really got interested/involved in custom rifles, I did like everyone else & started with a Rem 700. I no longer do this. Unless you already have a donor action, I feel you are at a disadvantage buying a complete rifle just to tear it apart. Unnecessary expendatures on a stock, barrel, trigger & bolt that won't be used for anything exept collecting dust.
By the time you buy a complete rifle, send it to your smith to have it torn apart, trued & basically completely rebuilt, you are at or near the cost of a custom action. And in the end, you still have a Remington 700.
As far as finding custom actions, you will need to go directly to the source or a retailer. They just don't pop up for sale all that often & when they do, they're gone in a heartbeat.
Search, Defiance, BAT, Stiller, Allen Precision, Borden, Surgeon, McMillan etc. They all make actions to accomodate any cartrridge you can imagine & even some you can't.
Hope this helps,