DCS,
I enjoyed the saga of your adventures, brings back old memories and let me relive some times with my dad. We were getting a TD15 International dozer out of a sink at the base of a hill on our place, he had dropped in onto the belly pan in about one hearbeat. Sure am glad you got it out especially ahead of the rain, "ah feel yo relief!"
That adventure and your pictures prompted me to offer this suggestion. I see there is a lot of small brush around the area and one way to combat the sinking of you boards is to make a mat out of a lot of that scrub before you ever put down the first piece of wood. Ends up working like a snowshoe and will substantially slow the rate at which the timbers will sink. That's what we did with the dozer, raised the blade, put an underbrush/treetop mat down, then cut the trunks of the small trees to build up cribbing to the bottom edge of the blade, after about two lifts we had the front of the tracks up enough to start building the mat for the small logs that went completely across. It took us a couple of hours, but we did get it out. The first time I ever saw the mat method used was in 1975 when a "little ole" D-7 with a root rake had to rescue a D-9 with 3" grouser extensions and a huge full "vee" clearing blade that had sunk to the belly pan in a sandy patch. Of course the D-7 version of the mat was downed logs, he built a nice pile then backed up on top of it before tying the winch line on, that way he was lifting up as he was pulling out. Worked like a dream.
As far as using the bucket and chains and bending the bucket, yes in a heartbeat (don't ask) if it has not been set up to take it, mine is now reenforced under the front lip with a section of 1-1/8" oilfield polish rod and a 3/4" sucker rod laminated in behind it. That said, if you had a pair of chains you could hook to the bottom edge at each side, run the chains back along each side of the tractor, then curl the bucket which might get you a foot, use the come-a-long to hold the progress then uncurl the bucket, take up the slack, and do it again. Looking at your pictures it appears 5 feet would have been golden. The problem is having two chains long enough and then having something to anchor them to. Which reminds me, it is about time I go ahead and get myself a couple more 5/16" transport chains.