"I've been thinking of moving my cassette deck to a location between my JBL 4408 monitors, which are definitely not magnetically shielded. Should I be concerned about magnetic fields from the drivers causing any long term effects on the heads of the cassette deck?"

Probably not, assuming the deck will be at least a foot or so away from each speaker. Dragging magnetic tape across your tape heads (and other transport components) will cause way more magnetism to build up on them than being located in a magnetic field of this strength. Proper and regular demagnetization will take care of this. The only concern I see is for the tapes themselves. We all know that loudspeakers can damage magnetic tape, but it usually requires the tape being in very close proximity to the driver's magnet for this to occur. Again, once you get a foot or so away it's probably not that big of a deal. But of course this depends on how strong a magnetic field the given speaker produces. I would recommend taking a recorded tape (one that you can spare) and place it in the intended location for a couple of days. Use your system as normal and then playback the tape and see if the signal has degraded at all. If not, you should be fine, but I still wouldn't leave tapes near those speakers any longer than necessary.