The M24 is a good rifle, but a good gunsmith can get a regular 700 shooting just as good. If you were wanting to replicate the M24 then I would not even get the rifle smithed. Too much cash. I like the M24 but because the long action it makes feeding difficult sometimes. It is a very accurate rifle for sure. I wish I would have been able to use the new M110 before I retired. Semi-auto, with a silencer, and supposedly more accurate than the M24. Money
You can get an M24 without the deployment kit for about 3k I do believe, but if you just want a real good shooter, the 700 you have should be great, but I would rip that BSA off and throw it in the dumptster or use it as a trot line weight and get better glass. A good rule of thumb to live by is to spend as much or more on glass as you did for the rifle. not saying that your stuff isn't good, but if you want great accuracy, get good glass with the best scope rings you can get (Badgers or the like) and reload your own rounds till you get a load that your rifle likes the best.
A sniper rifle is like a guitar. You can buy the best, most expensive guitar on the market, but if it is not tuned and you do not know how to play, it will sound like garbage. Many people can shoot, a lot of people can shoot great, but you have to shoot better than that (and often) to drag out the potential in most rifles. Good glass and the right loads will do that better and cheaper than a gunsmith can. Learn how that rifle shoots clean and fouled, cold and hot, in rain and sun, and in summer and winter and keep a log of it all.
You might know all of that already, but hey, someone might not. I used to be a marksmanship instructor when I was in the USMC (before I crossed to the dark side(Army)) and most all of the problems I ever saw was the shooter, no matter what the skill level. I may not know everything about shooting, but I know an awful lot about it.
ETA: I would store that rifle with the scope on it. The scope should be torqued to a specific ammount and left unless you have a throw lever mount. Also, I wouldn't store it in that case, the foam traps moisture and can rust and pit the metal on the weapon, no matter how much oil you soak the foam in.