I understand the issue with undo'ing the strap and then attaching the tripod plate each time, but i dont know if my system has a solution (Giottos MTL9351B, and Giottos ball head) or if what your suggesting fits.
What's the model of you ballhead? It seems that some are Arca-Swiss type and other are not. At a quick glance, the ones that have a lever for the release are not, and the ones that have a knob to tighten the clamp use Arca-Swiss compatible plates. FWIW, most of the better heads use AS-type plates (e.g. heads from Wimberley, Kirk, Really Right Stuff, Markins, and of course, Arca-Swiss). The nice thing about that system is that you can get heads, plates, L-brackets, etc. from any of them, and they all work with the others. As you saw from that post, I just recently replaced my Manfrotto QR plates (they use their own designs) with an AS-type system. In fact, today I sold my set of Manfrotto clamps, RC2 plates, and BlackRapid FastenR-T1's.