I find it odd that you are restricting yourself to 200 yards when I routinely shoot to 800 with scopes less than $70. It takes more than a couple dozen MOA to make that adjustment, and I don't lose zeros.
I really think that quality trigger time and quality reloading time are worth much more than a fancy scope. I can't tell you the number of times that the guy beside me is banging away at 50 yards with an extremely expensive gun and scope, and I am working with a 1942 Mosin-Nagant or a homemade put together 7 mm08 at 200 yards.
If you can hold a rifle still and shoot a 1 inch 100 yard group or better, then a zeroing scope is about four shots:
Large blank sheet of paper at 25 yards, scope properly installed with nothing loose, one shot at center dot, re-aim rifle at's the · and have someone else turn the turrets until the reticle rests where the bullet actually hit. If you want to be fancy, do the corrections for scope distance above centerbore
Repeat at 100 yards.
Now fire a shot and it should hit very close to the center aim point, Adjust by noting the error and correcting the Turrets the required number of MOA.
Final shot to test
I once helped out a feller who had shot almost an entire box of shells, and I discovered he was merely moving the plastic return-to-zero controls, not really moving the scope aim point at all! Boy was he a frustrated feller!
We had him zeroed in about 5 shots.