I have just started with Joomla and so far it seems to tick most of the boxes. I am currently putting together a custom template for a site. The way I did it was
1) designed the site in Photoshop
2) Cut a static HTML make from the Photoshop layout
3) I looked at one of the existing templates and used it as a basis for my template, copying the calls etc. from it to my static page.
So far it's all working really well.
As for the flash site:
1) If you can do what the customer wants without flash, then I wouldn't use flash at all
2) You idea to overlay the div may not work. Flash loads as an object in the browser and you may have difficulties overlay it (I don't use flash so I am only supposing here).
HTH,
JC