I have been "banana peeling" on my mats too! My fix is to attach 2X4 cleats to the bottom side of the plywood sheets . Run the cleats horizontally, and stagger along the length of the plywood. For the 2x4s only attach shorter (16" to 18") pieces. Do not put 4' long piece of 2x4 across the width of the plywood because when mats flex the "cleats" will simply pop off the screws.
Also use 2" star drive screws (3\4" Plwood+1.5"for 2x4). Attach the cleats off center and not near the edges (Especially the top and bottom edges of the plywood as you are overlapping the sheets in the run and they wont bridge flat) Think of the design looking like a climbing gym wall layout. i.e. 1 cleat to the left, skip a foot, then 1 piece to the right, skip a ft. and repeat.
Use the star head screws because if you want to remove the cleats later it will be easy. If you get the plywood wet it will swell, plus add some dirt, thus burying the heads. Nothing is easier than to shove that star bit in there cause it will bite for removal. Forget philips heads they will strip. The star heads will be re-usable for next time you need cleats.
Lastly and most importantly DON't Go Down any Path that:
1) A tow truck cant pull you out of! Meaning would a tow truck have the angle and leverage to pull you out? Would the tow truck get stuck itself? Does the tow truck have a nearby tether lined up with the angle to pull you! A big nearby tree to tie off to? He is big and has stabilizers, but will he spin his own wheels after he gets you out? If he doesnt have any of these he ain't touching you!
2) Although guys are throwing ideas of items of what to lay down, a lot of what I am reading sounds untested and may not work SO use your head and don't try them when you have no time to test! Save those ideas to try on a short run where you know you can get out, not the 60' ft you have for this job.
The idea of laying down chain-link fencing sounds good, but I also think it will sink unless it is on top of plywood. But that type of fix won't solve the banana peeling problem you have.
Good luck! and don't be afraid to bail on the job or do the job with other equipment! 1 or 2 days stuck = no income, plus a big tow bill!