Keep A Driveway Usable In Wetter Months

Is your drive an easement where you HAVE to use the current location? I ask because it looks like with the slope of the hill it would be better to bear to the right of where you are currently trying to go up (based on the last pic) and go parallel with the hill instead of up the steep part. Might get you at least closer to the house.
Any chance you could get some creek stone gravel to use? I use mine alot for troublespots on the road instead of buying crushed rock. My drive is longer than yours and I don't want to be going broke just watching expensive gravel getting washed of it. I also have neighbors that say I can get all I want from their creekbeds. I happen to have a tractor with loader, but if I didn't I wouldn't be too proud to do like you...shovel and wheelbarrow.
Also, if you have a quarry near you, you can probably get some trash rock from them either free or very cheap instead of using the costly stuff. One you get a nice base established, then you can top it off with nicer stuff whenever the budget lets you.

Your road looks like mine originally. Flat roads and rain don't work. You've got to cut ditches to have the water draining off of it. And gravel higher than the surrounding land.

Gravel isn't that bad, if you buy it and haul it yourself. I can get a couple tons of sb2 for around $30... I try and put larger baseball sized rocks in 'holes', and then put the finer crushed rock (sb2) on top. Only 'issue' is you have to unload it all by hand... flat shovels come in real handy.

Back when I was dead flat poor, I'd pick rock out of ditches, to put on my road.... after I discovered the local construction yard had gravel/stone/sand, it made more sense for me to go and pay for a load on my 7.5'x18' trailer, and haul and unload myself. Even if the rock/gravel/stone were free, I'd still pay the other folks... as it'd take me an entire day to load that much gravel by hand/shovel. Cheaper/more efficient to buy it.

If you can't afford gravel, you're busted till summertime

Most of my road is still just rocked/graveled in the ruts only. I have gotten hundreds of 4 gallon bakery buckets full of nasty grease, and poured this stuff directly on the dry dirt/clay... turns out, this stuff will make the road 'waterproof', like an 'oiled road'... as long as I don't drag a log over it, it'll stand up to anything.

I dug quite a bit of my ditches with a shovel... great exercise!

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Mostly anything permanent needs to be done when the road is dry. Unless you can follow the good advice above, anything put on top of soggy ground usually disappears into the mud.
For the moment, you might have some luck with water bars to drain out the ruts if you have a slope to drain water away from the road. Water bars are irritating but they do work in the right place to keep a dual creek from flowing straight down the road. Ditches on both sides where the dirt is piled onto the center of the road helps.
But little is going to work once the dirt is churned up with use.

I had similar problems, one with our drive and the other in front of the barn entrance.

On the drive I did as you have been doing for a few years, i.e. continually add gravel. It never worked for long.

At the barn entrance, I also added stone for awhile. It didn't work that well either.

Then, with reference to the barn entrance, I decided to do what one does not want to do with a pasture, i.e. add too much agricultural lime at one time because it makes the ground hard. So, I brought in a load of sawdust, topped that with 2-3 inches of ag lime and topped that with the same gravel I'ld been using. I noticed a significance difference and did it again. Now that area has been "HARD" for over 6 yrs.

With reference to the drive, I did the same as I did with the barn entrance; however, it did not work there. I learned it is because there is not a strong hardpan under that part of the drive; so whatever got placed in that spot, gradually sunk! This is when I used geotextile sheeting. During a dry period, I dug that area of the road down about 18 inches, covered the entire area (including up the sides) with the sheeting, placed large (12+ inches) rock all around sides and over bottom, added a layer of smaller rock over that, continuing with graduated rock until hole was filled. Then I put the soil back over the area and let it sit. When I get enough money, I will place "crushed run" over the entire drive, including that part, because it has not held water now for over 2 yrs.

Hope this helps. (I might add: The driveway is higher than its sides.)

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The reason you have seen the twin rock trails work is they kept laying the gravel down till they had a firm base that was level with the surrounding ground.
If you could see how the ground looked underground the gravel would look like upside down mushrooms with the stem part being the trail.
What you need for a good drive is dry soil.
The traditional way to do that is with ditches on both sides that both intercept water before it gets to the road and drains it from under the road.
Gravel in the drive helps drain the area under the drive and spreads the load of tires across more soil.
The geotile fabric people talk about helps contain the gravel.
Something you might try if you have limited resources and lots of labor is to take a tile spade and dig a 18 inch deep 4 inch wide trench where you want the tire tracks to go. lay in plastic corrugated Drain tile at the bottom of the trench and back fill with gravel.
remember the tile has to have a down hill slope so it can drain and should empty out in a place where the water it collects can drain.