One possibility would be to add a bevel gear to the side of the flywheel and another to the side of the hand wheel. next you would use 2 idling bevel gears and 1 fixed one. on a shaft that would extend from the flywheel and past the top of the bevel gear on the hand wheel.
the fixed gear on the vertical shaft would turn the shaft all of the time the flywheel is spinning.
Now both of the idling bevel gears would remain in contact with the bevel gear on the hand wheel one above the center and one below they would need to be stop collared in place for them to remain in mesh contact .
Next a drive spool or clutch spool will need to be keyed to the shaft this needs to be between the 2 bevel gears
friction disc will need to be attached to the spool on both ends to contact disks mounted on the 2 idling bevel gears. a linkage system to raise or lower the spool to make the friction disk contact either gear this will give you the ability to make a single stitch or a run of stitches in either forward or reverse. figuring out the gear ratio will be the final piece to this drive system
In effect I have described how the forward and reverse works in small outboard motors some however use dog style clutches instead of friction discs
Just one suggestion now lets hear others.
This type of drive is both simple and easy to construct.
I used the term bevel gear as generic when the term miter gear would have been more accurate in this case I suppose