No "finagling" required to get the 1581 to read PC-formatted floppies. It's an MFM drive and the code is built into DOS to read it DOS-formatted. It's not native, but it can do it with the right commands.
How would the 1770 (or 1772 in some models?) react to a gapless track? Would it be possible to just keep re-reading the track and capturing chunks of the data stream?
Get the track sync, read 512 bytes. Get the track sync again, read the next 512 bytes. And so on. My guess is no, since it would seem the data would come from the disk much to quickly to "stream" and the controller would essentially buffer then DMA the sector to drive memory.