Our Hybrid Forum is really the best place to ask on specific wiring issues for both of your scenarios.
In fact, you could just part out the Integra, and use the funds for a GSR swap for your hatch.

In any event, take a moment to swing by the Hybrid forum and the specifcs of wiring will be revealed.
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Regarding the transmission: The GSR's higher final drive will be a better match to the powerband of the B18C* motor. Ideally, you should get a GSR tranny... but if memory serves, a LS manual will fit. (I think)