What mods are required for the transplant?
The details vary, depending on what commission number the gearbox came from, and what it is going into. My case was probably the most extreme, since I put a later TR6 gearbox (with TR4 OD) into a pre-TS50000 TR3. It's been awhile, so I may have forgotten one or two things, but here's what I remember, not in any particular order:
1) A late J-type OD won't fit without some major modifications. You'll have to cut away the frame tabs for the rear crossmember, and fabricate a new crossmember farther back. I haven't tried it myself.
2) The 4-synchro boxes are about 3/8" longer (with or without OD), so either drill new holes next to the old ones in the rear crossmember, or use a round file to elongate the existing holes. I also had to bend down the flange on the back of the crossmember, so the mount wouldn't hit it.
3) Late TR6 will need the speedo drive gear changed (original gear makes the TR3 speedo read about 10% low).
4) You may need longer mounting studs at the top of the engine block. Length is kind of critical with a late TR6 box; if the studs are too long then the tail flange may not clear the body on installation. I didn't find ready-made studs that would fit, so I made my own and wound up having to trim them to get the gearbox in.
5) If you keep the TR3 clutch, also keep the throw-out bearing & carrier that go with it.
6) I had to shorten the pushrod for the clutch slave by about 3/8". That left the slave return spring too loose to return reliably, so I made a little mounting tab for it to restore the original length. (Most people might not care about this step, but I want the clutch to engage at the same pedal position, every time.)
7) This is purely optional, but I did not want to lose the dipstick/filler hole on top. (The TR6 gearbox is normally filled through the side, from under the car.) So I rebuilt the TR6 shift linkage (rails, forks, etc.) into the TR3 top cover with the dipstick.
8) If you don't do step 7, you may need to drill out some tapped holes in the TR6 top cover to install the TR3 shift lever. (Or just use the TR6 shift lever, but I don't like the longer lever with the bend in it.)
9) If your TR3 is before TS50000, you'll need to modify the tunnel to clear the starter bulge (or find a later tunnel).
As a side note, the mainshaft for the A-type OD will not work with the late TR6 gear set. It might be possible to have ORS (in the UK) make you a custom mainshaft to suit; but instead I opted to use an earlier gear set in the late housing.