The boats I frequent do... which is one reason I frequent them. Ex: Peace, Magician.MHK:2) Most of the boats in L.A. do not pump Nitrox on the boats, so as a result if you show up with a Nitrox filled tank for dive 1, and when you need a fill afterwards you'll be pumping regular old into a Nitrox tank;
As for the second part, this strikes me as an issue only if you are trying to maintain an oxygen-clean tank (for use with PP blending methods, vs. membrane or stik). And the issue then would apply air or nitrox... no local boat I know of hyper-filters their plain air to modified grade E standards anyway, so you'd be nuts to bring that tank on the boat anyway, even for air. The Sea Bass may be an exception, as I think they use PP blending for their Nitrox. That said, I wouldn't get Nitrox on the Sea Bass, as I don't have the patience (or spare tanks) for oxy clean and PP blending... I'd rather just dive air than deal with that hassle.
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Anyway, this is besides the point. Sounds like a fun trip regardless.