Clearly your problem is the plastic lip preventing you from sliding on a replacement rubber.
My guess is the original manufacturer must have got the rubber grip on somehow, and I would expect the plastic lip to be a separate part added after the rubber grip was fitted. It could have been glued on or push fitted. Have you tried removing it, if it won’t come off, then as it’s plastic, just file it down to the same diameter as the rest of the grip.
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