Yeah have seen the tires alot. One oldtimer around here had a whole truck dedicated to his lawn saver he used to call them.
He sold pine logs to the mill, and I swear HE could land 16 foot logs perfectly flat no matter how high or low he was.
He upgaded to some big tractor tires that some one gave him and actually bounced a log onto his log trailer. So I've been told. This guy was extreme in every way.
We were working for an older couple last year and he started telling me about the old tree man. He told me about the time winched his little wagon up onto the tree and strapped it on like it would be carrying a log down the road, then got down dropped the log with wagon attached and hitched to his truck and went straight to mill.
I use the "track mat " version....pretty burly if you ask me. Heres a pic and vid over a asphalt drive. 200 per sheet, local supplier in Charlotte. Super bike tires under, nice and light..
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Like MB, I use a layer of brush to drop the logs on. I leave the final spar as tall as can be safely dropped from the ground. We clear the brush, use the logs already down to cushion the drop of the spar.
2nd alternative, use a rope. Carrying around tires would be too much for me, but if I did, I would place the plywood on the ground first, use motorcycle tires like No Bivy and lay old carpet on top of that, or just four layers of carpet with no tires on 2 sheets of plywood. I'm sure you will be able to find a source of old carpets. You may even be able to get a few dollars hauling it away.