Is there any particular reason you're strying to strip the paint from the 2x12 framing joists? these will be covered when you install the new floorboards right? I would just leave them alone. The only reason I can imagine that you might be stripping these structural parts of your deck is that your deck is aecond story deck. if this is the case, you could just use a solid color latex stain and stain them close to whatever color stain you plan to use on the deck.(By stain on the deck, I am refering to anything from a Thompson's waterseal...to a Flood CWF or a semi-transparent stain.) Whatever the case may be, you could turn this difficult stripping problem into a good opportunity to transform the underside of your deck in a beautiful compliment to your deck.
As far as what to do on the painted posts....if you don't like the accenting solid color stain idea, you could always 'wrap' them in 1x6 cedar boards or whatever type of wood you plan to use for your floorboards.