There are only 2 factory distributors that will fit the 368 Lincoln/Mercury engine that use both mechanical and centrifical advance.
Those are the 57 units. One has a tach drive and the other does not.
Both of those units are a one year only "trick pony".
And yes pretty difficult to find.
I suggest acquiring a 57 and later Ford distributor and changing the distributor/cam gear with your existing Lincoln unit.
This way you have the desired mechanical and vaccum advance systems to work in conjuction with the later carb.

If you do decide to sell that 56 Lincoln carb - I would be interested in it.

Oldmics