As you requested in the Steam workshop, I am reproducing my bug report in this thread.
System: PC
Expansions: Have G&K + BNW
Legalism: Legitimate game from Steam, fully updated with the latest patch.
There is a huge problem when upgrading heroes to sea units. At the moment they are upgraded, you can briefly see the vision of the unit expand from its embarked land unit vision to a full ship's vision, but this only lasts for a split-second before going back to the same vision it had when embarked. From that point on, the heroic sea unit retains the exact same vision, lowered defense, and slow movement speed that any embarked land unit has, which is pathetic compared to regular sea units.
I am nearly certain that I already know what the problem is, but I will provide you with the log as well. It seems clear to me that the reason this is happening is that heroes keep all of the positive or neutral promotions they had from the previous unit when upgrading to a new unit. For this reason, the heroes keep the embarked promotion even as a sea unit, which overrides normal movement, defense, and vision rules.
The nice thing about this is that it lets me do things like upgrade to submarine, then upgrade to infantry to have a powerful land unit that has a 75% attack bonus and is invisible to enemy units. Not sure if this was an intentional feature or not, but I like it.