Your list looks fine but here are a couple of ideas to consider;
1. Check out the action wrench sold by Northland Shooters Supply. I don't have experience with the Wheeler wrench but the Northland wrench works well.
2. If you're not on a tight budget, consider ditching the smooth barrel nut and replace it with a new one that has the square notches. Instead of buying the smooth nut wrench, you would get the notched wrench. I removed my smooth nut with a pipe wrench and discarded it.
A small shank barrel nut will measure 7/8" in length front to back. A large shank nut measures 5/8".
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