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Your description usually indicates a blocked vent. I know you say it's only 2' from the stack but that's what your description indicates. If you're on a septic tank I'd suggest getting the tank pumped.
Well, given your lengthy description (2 new toilets, flushes ok with a bucket etc)the only likely explanation is a venting issue. By that I mean the plumbing vent for the toilet drain. The toilet may be close to the main stack but the stack is not or should not be the for this toilet. At the basement it's a waste stack not a vent stack. The toilet should have a separate vent pipe which may be clogged.