I consulted the comments under the layout and changed the oscillation pot from 100K to 2K and for a bit more "spittiness" suggested in another comment, swapped Q2 from an MPSA18 to a 2N2222, which appears to have made a fairly subtle difference.
Much more usable as a consequence, so I'm going to consider it "done for now" and box it up when I have a minute.
Hurrah!