Getting back to your original requirements, Getting unstuck at minimum cost, I'd vote for the Hi-Lift. You should have one of those along anyway.
Prepare the truck for the pull by jacking up the worst corners, sticks and stones under the wheels, and the pull would probably be well within the capability of the Hi-Lift. Use the shovel, too.
But consider this: the hard work part of the pull is the jacking of the jack for three feet, then re-rig and start again. Half of your effort will be taking up the slack every time, the stretch in the cable or straps!
Use chains. Put some hooks on the jack, one to the top of the beam and one on the lift. Equip yourself with at least 3 lengths of chain (5/16" is not expensive) and use the Hi-Lift hooked in anywhere along the length to "shorten" the chain length. At the end of each pull, use a short length of chain to bypass the Hi-lift, then back off against that bypass chain. That way you don't lose the pull you just did. That works going up hills, too. And, chain does not stretch like rope, cable, or straps do. Then Re-rig the Hi-lift to pull another 3 or 4 ft (get the 60" Hi-Lift).
You'll want to rest the Hi-lift on something to keep dirt out of it.
My wife and I did this with our old Jeep M-38 one time and conquered a 200 ft 45 deg slope. Saved us many hours of driving 'around'.
When the time comes that the cost of a winch is affordable, you'll be ready for it LOL. But the Hi-Lift and some chain will get you out of the emergencies.
Bob