I know! Haven't done it yet, but some day. Maybe. Only the Laycock J-type overdrive fits. Even then, you need a screw jack to belly-out the tunnel slightly from the inside. Since the Midget crossmember is right where the overdrive needs to be, you need to open up that area first.
Standard procedure seems to be to open the inspection port up to the crossmember, and cut the center section of the crossmember out. Two-inch square stock will fit into the open crossmember ends to reinforce them, then you attach two-inch stock underneath the crossmember all the way across, with a "tail" extending back to the tranny mount point. (Some people weld the whole thing in, but at least one conversion I've seen bolts the crossmember in like a subframe, which makes getting the engine in and out much easier, with no loss in rigidity.)
I'd think it would have been really easy to fab up a mass-produced subframe at the factory that would have enabled the 1500 Midget to have the overdrive right from the start...I can only figure that BL was figuring on killing the Midget in favor of the Spitfire from the very beginning, and didn't want to spend a penny more than absolutely necessary on it.