PS,
Welcome to the forum.
I can only give you some ideas for Colorado. I presume you are looking to rifle hunt since you did not say archery. Most of the state is over the counter for elk licenses. You can purchase the licenses and hunt in one of the units that is open without having to accumulate preference points. Those are good for either the "second or third" seasons. Another option that you have is the first season which you have to apply for. It is mid October and you have a chance at catching animals in their summer areas. No deer hunting in the first season though. There is also a fourth season that is focused on cows rather than bulls, but bull licenses are available. Very few units open to 4th season deer.
I don't give you much of a chance drawing into any of the quality units Those units take anywhere from 7-?? preference points. That doesn't fit with what you have described.
Success percentages vary, but statewide you are looking at ~25% at best. Significantly less than the 50% you are looking for.
Check out the DOW website for information about hunting in CO.
http://wildlife.state.co.us/index.asp

I think CO satisfies the other requirements you are looking for. I do not know about other states.
Good Luck

I posted this same answer to another fellow but.... look to NM. You have decent odds and if you d onot draw, you can buy a landowner tag for a reasonable price. If you are serious about WY, get in the draw this year to build points. As a SD resident, have you tried for an Elk tag in your backyard? I know they have left over cow tags that could get you a "trial run" per se on hunting Elk. I deer hunt by Hill City every other year and see Elk quite often. Build a few points in Co and get an easier to draw unit. I wouldn't go OTC if you haven't hunted Elk before and do not know of a honey hole.