Thanks for the info everyone. I am leaning to the 22-6mm since it looks like that is about max case size for the bullet weights I am looking at.
My dad has had a 22-6mm for 20 years now. I've shot it on and off since he had it built and between the two of us it has dispatched countless coyotes. Couple things you'll want to keep in mind before you have one built, if you haven't already done so.
Are you building this on a short or long action? If you want to get the full use of the case capacity and shoot the heavy for caliber bullets, it needs to be built on a long action. Ours is built on a short action Rem 700 and it has a Wyatt's extended mag box which allows for a longer OAL. We shoot the 75gr Bergers and even with the longer mag box, it is barely long enough. If we were to shoot heavier, longer, bullets like the 80+ grainers it would be eating up case capacity. Another option, if you are using a short action, would be to have it throated however long you need, but then single feed and shoot it as a single shot.
The other thing to keep in mind is brass availability as well as the quality of that brass. Pretty much the only, new brass, that is available is Hornady and IMO their brass is just mediocre at best. Others may feel differently about Hornady brass, and that's fine, but if someone believes Hornady brass is good, they must be comparing it to some really crappy brass.
I'm certainly not trying to talk you out of anything and into something else, but the 22-243 is a ballistic twin to the 22-6mm and with not only top notch brass, but it works far better in a short action. Even though we have a 22-6mm and it shoots VERY well, I currently have a 224 Terminator build going on right now. The 224 Terminator is what my gunsmith, Defensive Edge Rifles, is calling their version of a 22-243 Improved. I'm generally not a real big fan of improving cases, like the 243, because they gain so little case capacity and it just doesn't seem like it's worth the extra time, but Defensive Edge offers formed Lapua brass for all of their Terminator cartridges for a small fee so that makes it a no brainer for me. Once the first 224 Terminator gets up and running, my dad is sending his 22-6mm in to them for a rebarrel and it will become the same, as well.