I don't know if I would class myself as a Moulton expert, although I have a 60's F-frame and an APB Land Rover, which is currently set up with drop bars and 1 x 10 gearing.
Some APB's have a braze on for a front mech, but I don't think the APB3 does so, as Mass199 says, you're stuck with a sinlge chainring up front.
Also before considering any changes to the gearing, check what the rear spacing is - with a 3 speed Sturmey it may only be 120mm in which case you're going to be limited to an old 5 or 6 speed derailleur setup or a hub gear of some description (Sturmey still make 2, 3, 5 and 8 speeds with ~120mm spacing). If it's 130mm, then no worries
I think the seatpost on old APB's is 34.8mm. You can get a shim from SJS
to use a 27.2mm post instead.
Lastly, you should defintely check out the Moulton group
on Yahoo. Loads of very knoweldgeable people there.
Hope that helps