Hi,
I'm not terribly knowledgeable about GT6, but have been looking into getting one (eventually) and have done a little research.
One comment I've often found is that the GT6 gearbox is perhaps the car's weakest point (some models also have axle issues). I've also seen some reference to installing a TR6 gearbox as a stronger replacement unit. So, if strict originality isn't a concern of yours, you might have a really great setup.
Personally, I'd keep the TR6 gearbox. It's a strong, proven gearbox that reached the peak of it's design in the TR6 (AFAIK) and might be easier to repair or rpelace, if ever needed.
There are also quite a few options for TR4A/TR250/TR5/TR6 clutches, since there were so many of these cars built originally and still on the road. By, comparison, far fewer GT6 were built, so unless it shares its clutch with other cars, might be harder to find clutch parts for, or your choices might be more limited.
There have been some issues with TR6 clutches. But many of these now have well-documented, developed and tested over the years as need arose. I don't know if the GT6 clutch was comparitively more or less reliable or problematic.
I don't know the weight of a GT6 gearbox, for comparison. But, the TR6 gearbox is about 75-80 lbs. The A-type OD, if that's what it is, adds another 30 or so lbs for a total of 120 lbs. approx.
You can tell if the OD unit is an A-type for certain by looking on top for the Laycock serial number plate. It will specify. It will also show the amount of overdrive reduction, the first two numbers of the serial number would be "25xxxxx" if it's 25%, etc., unless it's been modified.
On the other hand, getting to that serial number plate that means removing the gearbox cover, at least. SO, some other A-type clues include: A vertical solenoid on the LH side (most A-types, I think there were a few models with a horizontal one, but all J-type had horizontal solenoids AFAIK). External operating linkage at the solenoid (usually, some early TR2 or TR3 had an enclosed box, but those are rare). A large, brass drain plug in the bottom (bigger on the earlier A-types, still pretty large on later).
An A-type OD would be a bonus, IMHO. Roger William's in his various "Restoring Triumph..." and "Improving Triumph..." books really likes the J-type and recommends it. However, John Esposito at Quantum Mechanics, who rebuilds lots of the things professionally, feels the A-type is a more robust unit and recommends it over the J-type. Early A-type really pop into OD quickly and are prefered by anyone racing with one. Later A-type - which is what yours would be if it's early TR6 - are a bit softer and slightly slower shifting. J-type are a little softer/slower still. All of them can be modified for faster/snappier shifting, but that makes the rest of the drive train work harder.