You’re pretty late to the party for cow elk tags.
Do you have any points saved up or ?
I can’t speak for other states, but Oregon cow tags are
Pretty low and require lots of luck or lots of points. I don’t think there are any OTC cow hunts. Unless you archery and it’s a hair/either sex tag in the unit.
Start looking for private ranches or guides that have depredation, or damage control tags. I know Oregon is giving out a [bleep] load of cow tags to ranchers. But obviously that will be pay to play.

I’m doing cow hunt like that next month in Utah

All of them do something better than the 30-06, but none of them do everything as well.