Just a suggestion, not a cheap or free suggestion but a suggestion. Get yourself some road fabric or if you can, find it some old used greenhouse ground fabric that a greenhouse is getting rid of.
Lay the fabric in over your muddy areas and stake it down on the sides, bring in a dump truck and drop a little gravel over the cloth in the muddy sections. You might also work at the some ditch drainage or piping water away from your road. If you think it is challenging now, wait until you have driven over those areas for two or three years... lol...
Whatever you do, try to avoid putting organic material in those areas, clay passes and or runs off water pretty amazingly well, highly organic topsoil on the other hand does not pass water very well at all, it tends to become goop... I have dropped in waste hay on my driveway a couple times in the spring, it works great and gets me through a spring in a pinch, but I have to make sure and get it up and off of there before the next spring or it is mud slick and bogging time...
When you mention corduroy wood I assume that you mean branches set 90 degrees to the road across the road surface side to side. That would only work well with smaller trees and branches and even then your tires will tend to push down between branches and cause you "more" issues. I knew and old boy Henry Haun that worked on a road crew in "the New deal" during the depression years and they were building roads from cut wood rounds. Those roads were then covered over by rock and gravel though. To use rounds by themselves can be problematic as the wood becomes crazy slick when wet and driven over.
Whatever you do, you eventually want your roadway to be a bit raised from the surrounding area. You want something to keep you from sinking in mud, as I mentioned the road fabric or greenhouse fabrics, they have quite a bit of strength and will pass water while holding your stone up keeping it from sinking into your soil when the ground gets wet. You are also going to need to do some water control, find ways to drain the water from the road areas and keep it from collecting and pooling on or beside your road.
Anyway that you look at it, a driveway is generally not a "cheap" thing. When I bought my last farm 150 acres of dryland wheat farm and 50 acres of timber I had to build a driveway into the place. I had to cut out a 15 foot embankment on the county road to a "reverse" grade for 20 feet off the county road. I had been working for a place called Germer construction for about six months in preparation for all of this as I figured that as a good employee I would get a bit of a break for anything that I might need done. I asked them for a quote on the first 90 feet of my driveway coming off the county road.... they told me a minimum of $20K...
I went out and found an old 1942 2U D8DL cable blade cat dozer for $5K and had it hauled to my farm for $500. I then found a 67 Case backhoe and bought that for $3K and then I spent the next 6 months digging and dozing soil. I spent at least a couple thousand on diesel alone and then came time for the road fabric that was spendy but too bad I think I paid $300 for a 200 foot roll though keep in mind that was 17-18 years ago. The real spendy part became the gravel, I was being charged about $370 a dump truck load for gravel, after about four loads spring came and the county shut down heavy travel on the county roads so the company wouldn't deliver anymore. I noticed the neighbors who owned a logging company could run on the road all he wanted with full loads and found that the weight limits didn't apply to those of living out there. I went and picked an old 1946 GMC grain truck with a dump bed for $350, blew the engine driving it home and so I put an old 350 race car engine I had been building into it. (One crazy sounding dump truck, people would look from blocks around to see where that sound was coming from).
With that truck I could then haul 6 yards of gravel at a time myself but I had to drive for half an hour to get to the quarry. Each load would only cost me about $18 but the fuel was a killer as loaded I was getting around 3 to 5 mpg and empty I was topping out at about 8 or 9 mpg. It was still far cheaper than having it delivered and I was able to haul in rock when they were not able to.
As crazy as that $20K seemed to me, by the time I was done I had spent a good $15K to $16K building it myself. Though I had an old beat up backhoe, an old D8 dozer and an old dump truck to show for that money spent. The vast amount of time I wasted building all that myself on the other hand was insane.
LOL... Then a year later I logged some of the back forest and the guys brought in their equipment and offered to do anything I needed road wise for free.... Live and learn...
Roads are definitely not cheap or easy and you will get out of it what you invest into it.