I searched the usual places like Alldata and a few technician sites but only found one reference to anything like your problem and the cause was a dying battery.
It makes sense in a way. Most alternators reach max output somewhere above 2K rpm so if your main battery is shot, it might take that many rpm to feed enough current demands to make the engine run normally.
An electrical load test might help and imagine a DIY oriented auto parts store has a free tester.
If you do go with a fuel system repair, definitely do it outdoors and not in the garage.
Good luck.
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