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The key to this problem is, "When the gas tank is less than half full,...", and only secondarily, "...occasional hesitation hard enough to put my teeth in the steering wheel...."
The other suggestions, about fuses, electrical connections, etc., are only valid if the problem occurred at any level of the fuel tank. Only the hose problem -- a split or leaking hose that's between the transfer pump and the fuel line -- is predicated on the fuel level being at or below the midway point!
And I doubt that the intermittant failure of the transfer pump because of electrical problems would cause such drastic losses of power, since it's only an aid to the flow; on the other hand, air (actually fuel vapor) getting into the fuel line because of the leaking hose would definitely cause such abrupt losses of power!
It's a shame, though, that your mechanic was too lazy or incompetent to change that little hose when he changed the transfer pump. Now you have pay all the labor charges all over again to virtually repeat the entire job (that hose would have just cost 'loose change' if it was added to the original job). But on second thought, maybe your mechanic knew just what he was doing, after all [maybe he's got a kid about to start college?]!
I'd go to another mechanic.
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