I haven't been on WW in a long time, but I thought I could offer some advice as a guy that has been building towers for a long time. And a guy who has made a LOT of mistakes and learned a few things in the process.
To answer your first question about reinforcing: glassing in a plate such as kingboard, wood, or even aluminum is the best way to strengthen the tower mount areas. Its a tedious and messy job. Personally, I would pay an experienced fiberglass prefessional to do that since they'll have all the quality materials.
That being said, I don't think reinforcing your tower mounts are going to give you the results you are looking for. In my experience, this particular tower design is the culprit. There is too much distance between the rear vertical legs and the rear mounts of your tower. Adding to to that, the rearward lean angle is extensive which also translates into tower flex.
As Patrick suggested, you may want to consider adding another a support leg that attaches to the rear vertical legs and closer to the rear mounts. But I understand that will kill the look that you were going for. Alternatively, you could ditch the heavy speakers, but you already know that. I'm not trying to harp on your tower. I'm just trying to give you more information so you can decide what is best for your boat.