So I finally found some time this last weekend to pay some attention to my sorely neglected Z. I spent Sunday morning removing the strut tower bar, engine cover, and throttle bodies. From the outside it didn't look that dirty. But once I got behind it, there was black gunk all built up behind it. I hit some clean cloths with carb cleaner and went to work. It took a bit of elbow grease and I cleaned about 95% of it. After I reinstalled everything, the Z fired up perfectly. I also installed some new factory air cleaners too. The Z can now inhale a lot easier.
My hypothesis as to why my engine was shuddering during hot start up could be due to the gunk build up in the throttle bodies was causing the plenum to stick. When the engine was hot, the gunk melted and became sticky. That caused the throttle bodies to not operate smoothly. When it's not opening smoothly, that caused the engine to shudder and that caused the gauge sweep effect to not initiate properly.
That's my best guess. Anyhow, for those of you who have this problem can consult this nicely written DIY on the G37 board:
DIY Clean your Throttle Bodies - MyG37
So that's that..