Swift, I've hunted antelope in Wyoming a couple of times as a non-resident. We hunted in units in the SW part of the state which have a lot of BLM land and some good bucks, but the odds of drawing a tag are low. From what I understand, the units with the best odds of drawing a tag have the least amount of public land.
I live in Montana, but I travel through or to destinations in Wyoming just about every month. I don't think I've been on a highway in Wyoming that I haven't seen antelope.
I hunt antelope just about every year in Montana, and have hunted them in Wyoming and Colorado. All were DIY hunts. I have never been hunting them and not got a buck, and I have never taken a shot at 300 or greater yds. The calibers that you mentioned are fine for antelope.
As to your other questions,
1. ORV permits are not required for your car or truck that you drive on the main roads. Much of the BLM land is closed to off road travel.
2. Camping is allowed almost anywhere on BLM land. We camped on BLM land in eastern Montana on our antelope hunt this year. I think you can drive up to 100 yds off a road to set up a campsite on BLM land. We have never had a camp looted, but we don't leave anything of high value in camp.
3. Fall weather can be hot and dry, rainy, or snowy and cold...all in the same day. Much of the prairie "gumbo" gets very slick, and even main roads may become impassible with just a little rain or snow.
4. On the two Wyoming antelope hunts that I did, we only saw a couple of other hunters when we were hunting, and we hunted opening day. I think Wyoming antelope tags are limited enough that there are not crowds of hunters.
5. I think all of the Wyoming antelope units contain at least respectible bucks (13-14"). Yes, there are units with bigger bucks, and like the units with greater public land, they are usually the ones with the poorer odds of drawing a tag.
As to Wyoming's guide requirement for hunting in wilderness areas, this is a state regulation on Federal land. This regulation was enacted to protect the guide and outfitting business that hunt deer, elk, sheep, etc in Federal U.S. Forest Service Wilderness Areas. I do not know of any Wilderness Areas that have antelope hunting. A non-resident can hike, fish, or camp in any of Wyoming Wilderness Areas without a guide, but we cannot hunt there without a guide. It's Wyoming's regulation, and it's stood up in court, so it stands. Just my rant.
Hope you have a great trip and hunt, and kill a couple of good bucks.