Per my research (I do not have actual experience with the Z) 300zx OEM trannys are generally considered reliable up to 300 HP. Failures have been reported in the 400+ HP range. The transmission for both the NA and turbo'd zx seems to be the same except for the bell housing, so I think you're good to go. I imagine someone else with more experience could chime in.

Until then, here's a link to a similar converstaion:
how-much-horsepower-can-a-stock-z31-aut ... 99347.html
PS - congrats on the turbo upgrade. How is it running? Does it feel great?
PPS - welcome to the forums!
