Waiting for mud to dry
It has been a very wet year.
The truck has been stuck most
of the summer.
Today we got close to getting
it on its way....but it's still stuck.
Maybe tomorrow will be dry
enough?
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About us: Anna Hess and Mark Hamilton spent over a decade living self-sufficiently in the mountains of Virginia before moving north to start over from scratch in the foothills of Ohio. They've experimented with permaculture, no-till gardening, trailersteading, home-based microbusinesses and much more, writing about their adventures in both blogs and books.
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Heather --- I think Mark puts more time and thought into his four lines than I do into my four paragraphs. I'm glad you appreciate it!
Eagergridlessbeaver --- That would be a good idea...if the other vehicle wouldn't just get stuck too. Our floodplain is wet over a large area when it's wet, so the best option is usually to wait it out --- once the terrain is dry enough for another truck to get in there, it's dry enough to drive this one out.
The profile in standard road tires will fill up with mud very fast. And these tires are relatively narrow. The quickest fix would be to fit proper wide off-road rims and tires, I think. Provided they fit in the wheel wells; your pickup truck doesn't really look like a proper off-road vehicle. Wider tires result in lower ground pressure, and the coarser profile shouldn't fill up.
Another trick is to lower the tire pressure for riding off-road. This will also result in lower ground pressure.
But for your kind of terrain, a proper 4x4 would probably be much better suited. There are plenty of old Landrovers and Toyota landcruisers around.
A truck isn't much use when it's stuck.
You stepped right in the middle of a dispute Mark and I have been having for the last month or so. He wants some subset of: an ATV, a tractor, more heavy duty mud tires (although ours are already mud tires.) I respond that I've seen what four wheel drive vehicles do on similar terrain, and greater traction means you tear up the ground more.
I think the long term solution is just to keep plugging away at putting rip rap in the ruts since that's already working in spots we've thrown enough rock at. Meanwhile, just driving when it's dry enough to get through allows us to haul without making the driveway worse.
We've been in a bad situation this summer because the golf cart has been out of action --- it's light enough that it nearly floats over the ground, so it seems more capable of handling some mud if the surface isn't actively wet. We were slow about getting it fixed because we really didn't want to carry that heavy, heavy battery out to the cars and then back, but we finally did, so hopefully once the truck's out of the way, we'll be able to do light hauling with the golf cart.
The one idea I do like is letting a little air out of the tires to widen their profile. Maybe that'll help Mark get out of the spot he's in...
You should look at the problem from an engineering perspective;
Stating the problem
The problem to me seems to be that you want to be able to haul significant amounts of material (hundreds of pounds, maybe thousand(s)?) from the road to your land over difficult terrain, including a creek and waterlogged soil.
Relevant criteria
Off the cuff (but you can surely improve upon it);
For vehicles, the biggest contributor to road damage (using common sense) seem to be:
Possible solutions
Presumably you don't want to carry everything yourself.
That means you'll want to use something to carry the load. Either a draft animal or a vehicle. I don't know squat about draft animals, so I'll stick to vehicles. 
Building a gravel road (which you are essentially slowly doing) will improve the load bearing capacity of the road. But you've got to haul is significant amount of gravel. You might also want to study gravel road design, lest to have to re-invent the wheel.
According to the criteria laid out above, you want to minimize the surface pressure that the vehicle puts on the surface. Since you want to haul a certain amount of goods, for ground-using vehicles that means
At a guess, if you'd compare the loaded/unloaded weight ratio and of the golf cart and a truck, the golf cart would be superior, since it isn't made to reach high speeds or protect the occupants from high-speed collisions.
For a ground vehicle, a hovercraft has be default the largest prossible supporting surface area and the minimal surface pressure, but controling one is difficult and it require significant energy. Maybe hovercraft that is guided by a cable would work?
Another obvious way to eliminate surface damages is to not use a surface vehicle at all. What you do seem to have plenty are trees. So you could use the trees to construct an elevated zip-line or cable car to haul stuff. This will also circumvent the creek an floodplane issue. Things to think about are the elevation profile you want to cover. Hauling stuff uphill consts much more energy that haulig it horizontally. Maybe uou can offset that somewhat by using two cable-cars or balance weights like is done with elevators. Depend ing on the weight you want to be able to carry it could be a significant project, though.
Remarks
This is not meant as a ready-made solution for your problem; I'm just not famailiar enough with the situation and parts of the problem domain to do that. What I just wanted to do with this comment was to show a structured way of thinking about problems.
Doc --- Yeah, that does seem to be our experience with four wheel drives in our floodplain. We've got at least one stuck quite soundly there and it took some doing to get it out!
Roland --- That is quite possibly the best comment you've ever made.
Clearly, we should have discussed this with you before spending all month disagreeing, because it suggests possible solutions that will keep us both happy.
I think your problem analysis is right on track. In terms of criteria, I'd tweak yours just a bit (and reorder them to put the most important first):
Using those criteria, my first thought is that your and Mark's idea of better tires could definitely help if they are broader like you suggested. That would reduce the surface pressure at least a bit and let the existing truck do the job with the same amount of damage over slightly wetter conditions. My plan to slowly build up the road would do the same --- that would take a lot more work on our part, but can be done slowly over time. I guess Mark gets his tires after all.
Bigger wheels (larger diameter) will make the truck ride higher giving more ground clearance and a larger footprint, reducing the surface pressure. Wider tires reduce surface pressure without affecting ride height.
Probably the biggest obstacle is the size of the wheel wells on the pickup. Those will limit the size of the tires you can put in.
If you want bigger wheels than fit in the wheel wells, you might look into getting a suspension lift kit. This will give the vehicle more ground clearance, and would possibly allow larger tires.
Keep in mind that bigger tires will also change the gear ratio, lowering the engine RPM for the same speed. Another point to consider is possible legal limits on the height of bumpers and lights above the ground.