Nice job! The design looks great in general.
My concern about the general tree vs the race-specific one still holds: the general tree seem better on average than the race-specific trees. I still think you need to move almost everything out of the general tree to the race-specific trees, expanding them in the process, or runs are going to feel the same no matter which race you choose because of the superiority of the general trees. There's no need to provide generic options to players -- that's what the items are for. The skill trees are there to make different ships feel unique.
Additionally, I'd love to see some change in the pattern for slot expansion between races. Race A maybe is weaker on structure, and so would have a pattern of light-light-light-medium-heavy, whereas race B would have heavy-medium-light-light, etc.