Can't help you with the selection, but for a NA car, nothing crazy or custom, I would imagine any competent tuner can do the tune. Also be sure to have them tweak throttle map for better response and torque map to speed up the shifts. Setting the fans to run a higher duty cycle at a lower water temp will help as well.
The problem is the soft throttle cut when brake is depressed -- apparently you can't switch that off at all on the 37VHR. (However, you have so much torque at your disposal, launching much above 2K will just get you spinning wheels anyway...)
The work around is to have a switch installed that can toggle off the brake lights (search -- apparently widely done for 350's and a few on here with 370's). That way you can stand on the brake and throttle together and let off the brake whenever you want.
Allegedly ECUtek has a launch control option, but it is not a widely used tuning package for the Z... ECUtek has had better luck with the FR-S/BRZ than the 370.
Again, I don't think you can do launch control, but you can approximate it with a switch for the brake lights. As to the other maps, you can have different fueling and timing, but I don't know about the rev limiter... that might be global.
The 12's and up can start in 2nd (I think), but not older models.
Hope that helps