My agent experience is sh!te, so I can’t help much except to say that, so long as you don’t utterly muck up the cover letter, it shouldn’t matter hugely. I honestly believe that any agent who likes your work will like it regardless of the cover letter, and any agent who dislikes you because of your cover letter regardless of the quality of the work isn’t an agent you’ll like working with.
The synopsis, on the other hand… I hate those things. I’m not sure if I’m more Indiana Jones with snakes or Indiana Jones with Nazis about them, but I’m certainly one or the other.
Beyond that, you’ve done all the things I’d have done, but hopefully your approaches will work better.