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Toilets of this vintage are notorious for clogging up and what you're describing to me sounds like a common stoppage. I have the same toilet and I have to plunge it occasionally. It's also possible that there's something caught in the bowl and unless you used a closet/toilet auger (see pic) what snake you used probably just went right by it
Ok, then there still could be something caught in the bowl and the only other option is to pull it off the floor and check as well as running the auger through the bowl from the outlet. If you don't find anything or this doesn't resolve the problem then either the bowl is defective or whatever is stuck in there is not coming out or this is just a periodic clog that's common to this toilet.
You're welcome. Yes 1 piece toilets are a bear to wrestle with. We got a toilet jack so 1 guy cold set them without ruining his back. A defective bowl is the least likely but they do occasionally have an internal defect that doesn't show up for years.