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Could be ignition problem. Coil breaking down at temp? There is a thin film module (not exactly sure the correct terminology) on the side of the distributor that can break down at temp. The module can be tested at an auto parts store. Have them test it several times in a row to get it hot, but be careful not to burn it up by getting it too hot.
I think you are leaning toward EFI. I would suspect ignition first. Good luck.
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