You are required to use Honda Z-1 if your tranny is under some company warranty. In the case some other ATF is used, HMC will not honor your warranty if you have an issue with the tranny. Otherwise, you are perfectly free to use any brand of ATF as long as it conforms to (or exceeds) manufacturer's specifications.
Fully-synthetic ATF is NOT, per se, "thinner" than conventional, petroleum ATF. In many instances, the viscosity is actually thicker. It will NOT leak any differently than Honda Z-1. Most any synthetic fluid will work perfectly fine with a conventional oil. What you have heard/been told is a fairy tale, just a lotta BS.
Fully-synthetic oils withstand much greater temperature operating ranges, reduce heat, and lubricate far better, by reducing metal-to-metal friction. Decimal point.
I bought 13 (thirteen) quarts of Red Line D4, directly from their website. Cost was $9.95 per quart + shipping.
What I am in the process of doing now is four (4) drain-and-refill procedures to remove most of the Honda Z-1 ATF. Tranny system capacity on the V6 cars is ~7.5 quarts. On a drain, you get about three (3) quarts. After the fourth D&R event, you should (theoretically) have NO Z-1 left in the system. Realistically, maybe 5 percent.
While not mandatory, I would STRONGLY suggest you use the same ATF in your tranny. Consistency in methodology is always a good idea.
I am on my FIRST D&R, with approximately 3 quarts of Red Line in the gearbox. And I have noticed a dramatic improvement in the way my tranny operates.