I also like certain brand rifles, and am willing to do some work to get one to shoot better. The factory barrels can be hit or miss so to speak, tho all I've had have been plenty accurate for general hunting use (generally 1 1/4"-1 1/2" with loads they liked). If you want that next step up though, a truly good barrel is money well spent in my opinion. Yes, other guns may shoot better out of the box, but, if you like a certain type, then do a bit of work with it. It isn't simply a cost vs outcome/benefit relationship. If you're like me, you'd be thinking about the other gun while carrying the new one, and wishing the old one would do what you wanted it to. Other makes simply don't interest me for various reasons
You know the basics, and they've been mentioned. Decent bedding, you have a good trigger, have the action trued when getting a barrel installed.
The course has optimal guns, but I'd take it with whatever you have thats close, load the best long range type bullets, and go do it. The 25-06 would lob bullets out there. A 6.5-06 or 260 would do it, with better BC bullet choices, though in your case, that would require another barrel. Barrels can be set up like savages, to be switch capable. They've been done on other makes of guns. I'm having a Ruger 77 tang safety done as a switch barrel. At that point the cost of different barrels are buying the blank and setup machining cost, but no further gunsmithing cost to change calibers or for a new barrel if you manage to wear one out.
"Far better it is to dare mighty things, to win glorious triumphs even though checkered by failure, than to rank with those poor spirits who neither enjoy nor suffer much because they live in the gray twilight that knows neither victory nor defeat." -Theodore Roosevelt-