So would 80W-90 be too thick even if it's synthetic?
If it's 80W90, it might be to thick. The viscosity doesn't change just because it's synthetic (unless the numbers are different).
One other thing, synthetics tend to "clean" things up pretty thoroughly, and that can open some leaks that might be plugged with dirt/gunk now. So it's a really good idea to check the level frequently after switching from conventional oil to synthetic, and watch out for leaks and drips.
Most of the bad transmission problems I've had in my past were in the weeks immediately following a switch from conventional lube to synthetic lube in the transmission, and the leaks and low lube running that followed that. Now, I only change after a clutch change when I also change out all the seals on the transmission. And I don't experience leaks any more.
One good diagnostic indicator for transmission lube level is the temperature indicator labels that permanently change when they go over a certain temerature. One of those that indicates 200-250F on the end cap of the transmission will quickly tell you if you have a problem with the lube being low. With a full transmission, it will never go over 250F there. But if it's running low, it will get very hot on the end, especially on longer highway trips, and the label will tell you.