I am in the minority of those who anneal their gas checks. It takes any "springback" out of them, and if I do my part the checks almost appear to have been cast into place, you can even see a shadow of the sprue cut.
Count me on your team 358156 hp....... Almost always I used gaschecks fully annealed. Like all you say plus a flat base. Once in a while I'll use .22, .25, an especially .35 checks without annealing as they are pretty thin material compared to most other bigger sizes.
I almost always size with push through type sizers nose first. Nose first because I get better accuracy....Many sizers are made by me with a longer tapered section in them. I have an assortment of expanders to fit gascheck snug to my particular bullet. I always size gaschecked bullets with back pressure (nose pressure) applied. I lightly 'bump' the check as I feel the contact before pushing through. My checks are on as flat as the bullet's base is as 358156 hp states above with shadows of anything on base like sprue area although I will tolerate very little of that either! and I've been known to 'skim' bases in the lathe if they're not!
Now if we could just get Hornady to put an even skirt height on their high $$$ checks I'd be happy!
Pete