I didn't see you post what kind of performance you're getting with the way it's currently set up. If you are getting acceptable velocity and accuracy then I say give it a go as is, sounds like you are doing fine. I'm actually envious of your success. If it hasn't got any kind of bedding then I would probably have it done to help with consistency. Your rifle is more then capable of what you ask- 700yard elk & 1000yard predator.
My LR rifle started as basically the same as yours, just laminated .338RUM. I never even gave it a chance. I sent it straight to Kirby Allen. Do I like what I have, absolutely! Do I wish I would have given it a chance with the original barrel, sometimes. I just wanted to have something different, a LR .338 Edge.
As far as the budget, I have less total in my rifle then you have just for upgrades. You should be fine. The scope you have is a good one, just limited on total adjustments. Check it to see how much elevation you have to play with after initial zero, then decide whether you need to upgrade mounts and or rings.
Sounds like you (like the rest of us, especially myself lately) need to spend more time and energy (and money) into pulling the trigger at longer ranges instead of upgrading things that might not need upgrading. Practice for that 1000 smaller target-shot, if nothing else it'll make that 700 yard bull that much easier. Or build the rifle of your dreams. Just be warned, you will never be satisfied if you start down that road!
