I'll take little pieces of advice you've already been given, and just add to it and make it my own.
Stay with me to the end though, so I can try and tell you the really good way to do this. (at least in Tx. and Okla.).
First. Being in the ranch business almost all my life, I can assure you that in Texas and Oklahoma at least, most folks won't let you hunt if they do not know you because of all the past or present bad experiences they have had.
We've had road hunters kill a calf thinking it was a deer, and they were shooting out of a car window any way ! Windmill blades shot, winter wheat with pickup and ATV tracks through them, fence problems, folks just found walking around on the place with a rifle like they owned it ! You name it. The list is almost endless.
OK. This covers what I have learned about hunting others property since I was a little kid, and am now almost 59 years old. This is from My perspective and a rancher/or cowhand, and from all the old boys I know that are ranchers from west Texas and N.M on up to Oklahoma.
First Do call or contact rangers in the area you may want to hunt. Ask if the know of anyone that would allow you to come and hunt whatever it is your wanting to hunt. You seem to be mainly after hog and yotes, and must remember a great deal of this is at night, and ups the anty of your
un-welcome presence and fear of you shooting livestock. But lets look at a few things here, and I tell you
this info is "Straight up."
After talking with a few rangers in the area/s if you DO get a lead or two, then obviously persue them. "DO NOT"call the people. If takes a weekend drive,do that. Ask the ranger who says yeh, Old rancher brown is pretty good at letting folks do this and that. Then find out from him where rancher brown place is at and go visit him. It is real easy to say NO on the phone.
When in that area stop at a place or two or every place you go buy, that is in coyote/hog type country of course, and say to them as you drive in real SLOW, the same thing you will say to rancher brown. BTW Go alone. Do not take a friend or realitive. You killed your chances already... "Howdy sir, I'm (your name), do not say where your from
unless ask, ( that is if you live in a city). I was jst wondering if I could have a minute of your time. You see I like to hunt coyotes and bob cats, and hogs, and well, since I got out of the service (that will help), I just don't really know where to do some hunting for them, (do not say, I can't find a place, this gives the idea you been turned away many times before), so I thought I'd just drive around a bit and do some face to face asking for permission. And BTW sir, I want ya to know that although I don't have the $$$ for a lease or such, I would more than glad to help out here for a day or two with any chores needing done. Perhaps with some fence work, or haulin some hay, whatever you might need."
At this point let him do some talkin. He may just flat say "noI'm sorry but we just don't let any one come around on the place.."
Now do not sound pushy, but you can reply. "well I don't hardly blame ya mr brown, I know there are folks out there that will abuse their priveldge/s and not care of the place, but if I may just say sir, I am NOT one of those guys. In fact I give you my word, I would NEVER bring anyone else with me, and never tell a soul about the place, and only come when it is convient for you, and I truly mean it about my offer to help out around the place a bit, and I will only go where you say it is ok, even if that means on foot. In fact Mr Brown, I'd be proud to take you or your son if ya got one with me, I'd enjoy the company." (he won't beinterested in going, heck he lives there) but it is just polite to offer.
If you get a yes, well no brainer from there,
"AND KEEP YOUR WORD."
If you get a NO. This make two of them now, so thank him and say you understand, and BTW sir, do you have some ideas of who I might ask/" If he does great, if not, thank him again, and go to the next place. This usually ends in a
success If you stick with it and don't give up.
Next go to the local feed stores and talk to some of the hands in there as well, kinda the same spill you gave Mr Brown, and you would be willing to do this and that etc as per above here...
Try the smallest local cafe as well. Always good info there, as well as blink and miss ma and pa stores.
This one will get ya but it works. Go to the blink and miss town nearest where you want to hunt, on a wednesday night, or about 12:30pm Sunday and ask the Pastor of a couple of small churches.
NO I am not joking. Iam very serious. Maybe pop n at 10:00 and after service when folks are filing out, you can ask him, and he will even have seen you were there. (I in NO wise mean this to be sneaky or deceptive) Heck church won't hurt you/me anyway... Most Pastors in real little town hunt, or have vistited the folks in their church on their ranches and farms and know a whole lot more than you might think. That can be a real gold mine.
Also, when you go to any of these places to talk to rancher brown or the feed store etc. don't wear camo clothes or t shirts with a dead deer on it, or have a 1/2 dozen guns hangin around in sight in the pick up ! Ha. And for sure when you go to podunk church meeting. just jeans and a shirt will do. haha.
I tell you from being in this life style, and having been a guide for over 25 years, and knowing truck loads of ranchers and cowhands, and country folk across several states. These
ARE FOR A FACT, very good ways to get your hunting done. Be prepared for major rejection. But, if you stick with it, and do the leg work it most generally pays off, and I was NOT even kidding about asking the local pastors, they know more about all this tham most rangers ever will, they are dealing with these people all the time, and know a very great deal about them.
Just be hat in hand honest pard,with everyone you talk to and it will pay off sooner or later if you stick with it !
WOW ! you say hey amigo, what about your place ? Glad you ask. We are one of the places that have the iron clad set in stone rule that no one but no one comes across any cattle guard on the place.

Sorry. We been burn way to much. I am sure you are a really great amigo, but it ain't just me you would have to convience, and the rest of the bunch would politely tell ya NO way.
Not to worry. I promise you this advice is many years of knowing what works for the average city guy, or local boy who comes out to a ranch and presents himself in such a way.
It will pay off if you persist.
And when you get the YES, drop by the house and offer up some hog meat, or at least thank them and show them what ya got, or send some pics to them if it was to late at night to door knock, and send a Christmas card every year. No joke.
Try some places out around Bronte, TX, and Slver City. I don't know how far you want to go or stretch out.
This stuff does work. You got to stay with it, and do it, and be patient !
Good luck !
CanyonMan