Congratulations! You have an excellent rifle, chambered for a great cartridge, and fitted with an appropriate scope. IMHO, too may hunters over-scope their big game rifles. You were wise to stop shooting when you felt like you had enough. Over time the amount of shooting you can do without discomfort will increase, particularly when you begin shooting from field positions. Shooting a .375 for precision from the bench is an acquired taste; I would point out that match shooting is not really what the .375 was designed for, but I expect you already know that.
As you use the rifle, you might find some of its features aren't quite right. The LOP might be a touch long, the grip might crowd the trigger guard and rap the knuckle of your middle finger, and if the scope extends much behind the cocking piece, it won't be long before you get tagged. All of these things however are fixable with a minimum of fuss. A wood stock can be easily shortened, a finger deflector can be installed behind the trigger guard, the scope mounts can be changed to move the scope forward or back, or higher or lower, relative to the height of the comb. The idea is that as soon as your cheek hits the stock, the reticle is right there, without having to go on a quest to find it.
As for loading precision ammo, just keep the tolerances that you have control over as tight as possible, thats how you make accurate ammo, regardless of the cartridge. Pull a factory round and weigh the powder charge. The factory will almost certainly use a propellant that is not available to handloaders, but matching a powder to the factory charge weight will get you in the ball park. Neck size your cartridges, match the priming to the powder charge so that you have reliable ignition with the minimum amount of violence, watch the neck and bullet runout, then you're on the road to making precision ammo.
Once you've beaten that out of your system perhaps you can concentrate on making quality big game ammo, that cycles reliably through your rifle without having to fight the bolt, that is accurate enough to hit a large target over the range you intend to shoot from, and retains sufficient power at that range, and uses a game bullet that performs well given the size and density of the target, and the velocity at impact, so as to have a reasonable expectation of killing the animal with a single blow. Then get out and shoot that rifle, with that load, at realistic targets at unknown ranges, under a time constraint, from supported and unsupported field positions, in a variety of weather and light conditions. I think you'll find that far more interesting, challenging, rewarding, and relevant than attempting to shoot bug holes with your buffalo (bear, moose, deer, elephant) gun.