Might also want to check your coil packs. I had a coil pack that was going bad. My car would idle normally, but when I accelerated, my car would sputter like how you described. Get a fresh coil pack and swap it out one by one. See if that helps any.
*Actually, I should have read your post more closely. My car would sputter around 2500rpm, but it would continue to sputter all the way up the range. So maybe it is the pump.
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