What we *want* to do is have them simultaneously stop/start, but to record using the mics connected to them, so we can do an 8-mic, time-synced mix (I realize it may not be bit-perfect, but it will be more perfect than saying "Hit REC NOW!" to each other...)
That's exactly what it does.
(just clarifying what the others have stated)
If you both have R-44s, then setting one to MASTER and the other to SLAVE and connecting them with a stereo mini TRS to stereo mini TRS cable will simply sync the transport control functions, but not the sampling clocks. You'll end up with 4 tracks from each recorder, 8 separate tracks total. The sync feature on the R-44 takes care of the initial alignment of tracks between the two recorders. Not perfectly to single-sample accuracy, but probably close enough. The clocks can still drift once recording starts. Whether the drift is significant or not depends on the two particular recorders. If the clocks match well then you can record for longer before you notice any drift.
Crystal oscillators are somewhat effected by temperature. Although I doubt it would be very significant, your chances of them staying in close sync might be slightly improved if the recorders are kept at the same temperature. So it's a good idea not to leave one running in the sun and the other in the shade and easy enough to do. If anyone has the technical expertise to confirm or refute if this would have any appreciable effect, please let me know. It may have no real world significance.
FWIW, when I'm recording 4 channels and the R-44 is not an option (it doesn’t fit into my pocket), I run two R-09s and hit record simultaneously on both decks. Once aligned, the timing difference is very close and usually not a problem over the course of an hour and a half or so. Interestingly, the sync does not drift appreciably over the course of many, many hours when playing back from the recorders themselves- using the same clock for playback as recording. In that situation the differences between clocks essentially cancel out.