Both of those calibers/rifles will take moose and elk at long range with good shot placement. But, long range is subjective.
The Remington is more easily customizable due to the plethora of aftermarket parts.
I doubt you need to do anything to the throat to shoot the 180 Bergers as I shoot them from my 7mm Rem Mag Sendero without issue. The twist rate is something you need to verify. The Sendero has a 1 in 9.25" twist which is about right.
Otherwise, you might consider rebarrelling as a 300wm, 300rum, or 338wm, etc.
Either way, you'll want a good stock bedded to your action (Boyds/HS Precision); a trigger or replacement trigger (Timney/Jewell); 20 MOA picatinny rail (EGW/NF); tactical rings (Burris Extreme/NF); and good optics (Vortex/NF). I also like muzzle brakes
(Holland QD/Muscle Brake).
You also need to budget for all of the supporting gear such as a 1000yd rangefinder (Lieca/Swarovski), ballistics software, reloading equipment, brass, ammo, fuel, range fees, etc... and, the list goes on.
The good news is that with a decent scope and little or no work on your 700, you could probably get started right away. Premium factory ammo may allow you to do some practice. But, you will need to handload to be effective at 500+ yds.
Quality components are important. But, the person that puts it all together makes the difference. There are some things that most can do themselves such as replacing and bedding a stock and mounting a scope. But, for rebarrelling, etc., you should look for a good smith and discuss the project.
There can be lengthy delays. So, it pays to plan ahead.