I have access to 20 acres in Bastrop County. There’s a group of 8 does that will come whenever we put corn out, would shooting one of the older ones make that group avoid the property?

Nah. Shoot one then get a feeder up and running.

I always look for the big gray ones, more than likely they are older.
I also look to see which ones don't have a baby, but that's just me.

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I shoot the old menopausal doe’s because they don’t contribute anything anymore and they are typically the mean ones that run the mothers off.

I think you could with very little problem. However, when I decide to take a doe I know that I need to remove a younger doe or a older doe..Young doe takes less than two off the lease and taking an older doe will remove a little more than 3 or so off. Most of the hunters on my lease tried to take the older does which was fine with me. I harvested a ten point buck and when I went to pick him up, three does showed up within twenty yards from me to eat.LOL.