Twin charging the 370 would be a very interesting and costly venture. There are two ways of doing this. The first way is compound charging as the Lotus pictured is set up. This would be feeding the turbochargers into the supercharger. This would results in very high boost pressures. Remember 10psi from the turbo system plus 4psi from the supercharger does not equal just 14psi. In a compound charged system the supercharger would be further compressing the 10psi from the turbo system. Hence the compound charging name.
The other option for this system would be to use a bypass valve to allow the system to use the supercharger for the instant response in the lower RPM's but then switching over to the turbocharger system in the higher RPM after full spool up has occurred. Finding a valve that would work well for this, and flow enough air for the Z's engine would be difficult. In regards to this working with the GTM kit it would be tough with the Rotrex charger, or even the Vortech found on the Stillen kit. This would work far better with a charger that has the magnetic clutch in the pulley (think AC compressor) like some of the Mercedes, AW11 MR2, and the Ogura clutch units.
It does look like the GTM SC and Turbo could co-exist on the same engine, but i think the only way this would happen would be to take the compound charging route. In other words time to lower the compression. I would love to see it, but someone would need some deep pockets to pull this off.
For my money i think i would go with a twin turbo kit, and use a small nitrous shot to spool it (assuming it needed the help spooling). Usually once the turbo's are spooled they aren't going to drop out of boost until you shut down the throttle.
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