Ideally, the crossovers would be needed. In fact, on 1996-97 models the non-powered speakers are fed directly from the radio and have crossovers mounted on them. For rear tweeters, it's just in-series capacitors to cut off the low range, and the front 2-way speakers have capacitors and resistors. The DC resistance of the Infinity speakers, measured at the terminals, is 3 Ohm. This is true for all 8 speakers.
Aftermarket 3-Ohm speakers are available from Orion, if it helps.
Funny you say the door speakers are going bad. In my set, it's also a door speaker that needs replacement. The seller means to send another speaker but has hard time finding one. Maybe I should trust him on that. I made some progress towards converting to Infinity, just as a hobby project, but now I am more and more inclined to simply install quality aftermarket speakers. Then I'd sell what I have for spare parts: you know how much those speakers cost at a dealer (even at a "wholesale to the public" price).