Hi Arlie,
I'm a little unclear if you are considering an A-type OD only and attaching it to your existing gearbox, or a gearbox/A-type combo and replacing your TR3's gearbox entirely. Let me try to address both scenarios.
I believe the A-type will work fine fitted to your existing TR3 gearbox. In my TR4 I have roughly the opposite: a TR3-era A-type fitted to a 2000 gearbox (essentially the same as TR6 gearbox). No fitting problems to speak of (see below).
Using your existing gearbox will mean installing the OD-compatible mainshaft into the gearbox, installing the mounting plate on the back of the g'box in place of the tailpiece (to attach the OD) and drilling and tapping the top cover for the inhibitor switches.
So, if you are re-using your existing gearbox, the input shaft is the same and it won't be a concern. Also, the clutch will be the same, and not a concern.
Now, if you were getting a TR6 A-type OD already mounted on a compatible TR6 gearbox, yes, the nose of the input shaft at the pilot bearing (in the rear of the crankshaft) is a bit shorter. It still works, though. I had that issue with the 2000/TR6 era gearbox in my TR4 as well. I plan to have a special pilot bushing made to compensate, or to just change the input shaft at some point. But I know of a cars with similar setups where nothing was done and they seem to get by fine (Note: putting a TR2-4 gearbox in a later car would be a problem! The longer input shaft would cause problems.). The short nose of the later input shaft still is about 3/8" deep in the pilot bushing on the TR4 crankshaft.
TR3A and earlier 3-synchro gearboxes themselves are slightly shorter than the later, 4-syncrho g'boxes, but the difference only really shows up at the driveshaft and that compensates just fine with the splined section. You might have to slot the holes in the rear gearbox mount a little, but that's easily done during installation.
There might be some clutch issues with a TR6 gearbox mated up to a TR3 engine. I'm not certain of this. The main thing I'd be concerned about is the later used a different diameter throwout bearing, and I think it rides on a different diameter front gearbox cover. However, these are external items that probably could be swapped around as needed. It's possible, too, to change to the later TR4A-TR6 type diaphragm clutch, if you wish. What's needed is re-drilling your flywheel since the later, lighter weight clutch is smaller in diameter. However, you can find plenty of reference to problems with this clutch in the archives, so it needs to be set up carefully. The TR2-4 clutch, although heavier, is pretty sturdy and problem-free.
There are some advantages to the TR6 gearbox, if that's what you are getting along with the OD. It has a heavier bellhousing flange that's less fragile than the TR2-4A gearbox. Also, a TR6 gearbox would give you synchro on all forward speeds. And, at some point, not sure when, the TR6 gearbox was upgraded a little internally.
Basically, the early and late versions of the A-type primary functional difference is that the early ones have a larger accumulator piston and will shift faster/harder into OD. The later A-types were slightly "detuned" to make them more "pleasant". The earlier ones are a little more desirable for racing. The really early TR2 and TR3 A-type had a slightly different arrangement at the solenoid, with a full cover protecting the actuating mechanism, but it is funtionally the same.
I think the TR6 A-type OD still offered 22% reduction, but I'm not certain of this. You should be able to tell for sure by the serial number, which will start with 22xxxxxx if it's that amount of reduction. J-type were 25% reduction and have 25xxxxxx serial numbers. Both of these assume no one has swapped around internals and changed the OD's reduction ratio at some point, which can happen, but is relatively rare.
I'm pretty sure the press on ring gear will work, too. In fact, didn't Triumph go back to a press on ring gear on the TR250/5/6, after switching to a bolt-on gear midway in TR3 production and up through at least the TR4A? One question is what starter you are using or if any changes are planned there. The TR6 gearbox can accomodate the later style of starter, but that would mean reversing the ring gear so that the teeth are oriented properly, if it's currently installed for the early TR3 starter. (Note: with a modern "gear reduction" starter, the change wouldn't be necessary)
You can get OD conversion/fitting kits and the gearbox mainshaft from John Esposito at
www.quantumechanics.com, by the way. He would also be a good person to discuss all your concerns with in more detail.
Hope this helps!
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