Magic spinning triangles or Doritos stuffed in a Spitfire make for a very entertaining little car. 
As noted above, over about 90-100 HP the diff just is not up to the task. So unless you are willing to limit the twitchiness of your right foot (no fun) or replace differentials every time you fill the tank (even less fun) you will need to upgrade the diff. That is not as easy as it sounds. No, the GT6 diff is not any stronger. The GT6 and TR6 motors can both easily be installed in a Spitfire if you use the GT6 'bonnet' with its clearance bump. But, the amount of extra weight pushed way up front past the front axle centerline can change its ultimate handling characteristics in a bad way. Due to the extra weight of the glass, hatch, body panels etc in the rear it's not a problem when the motor is in the GT6.
The stock 1500 was known for all kinds of bottom end weirdness. I saw several of them break cranks right behind the center main. I think that's because the motor was originally designed to be 948cc, Triumph just kept boring and stroking that original design past its limits. Even though the main and rod journal diameters were increased for the extra power starting with the later 1296cc version, the block was just too flexy. Having said that, the ones that are left now are probably not very likely to break a crank. Bumping the compression (stay under about 9:6-1 to reduce detonation), balance the crank/rods/pistons, upgrade the cam, lifters and valve springs, headers, electronic ignition and carb upgrades are all good things.
On carbs, a single DCOE is probably the ultimate power producer for a street motor, dual DCOE's can be used but I'd not recommend it, you can lose a lot of bottom end power. But the DCOE is finicky, it was designed as a race piece and thus to be constantly tuned. For a street car I'd go with the Euro twin SU manifold and 1 1/4" carbs. It's possible to put MGB 1 1/2 SU's on that manifold but there's some drilling etc needed. 1500's came in European version 75-up black bumper Midgets with twin SU's also, so if you do an eBay search make sure you include the Midget in your search parameters. The single Weber 32/36 downdraft is an okay piece for a DD but it's not really the best choice for performance use, particularly because of the way the intake has the 'sink trap' design.
Spitfire suspension and steering is the cream of 1940's engineering, remember the Spitfire was basically a different body on the Herald chassis. That doesn't mean they can't be made to handle. I too am not crazy about PRI's bolt on rear suspension, it just has a funky camber curve. By the time you do all the stuff necessary to turn a swing axle Spit rear suspension into something with decent geometry, you are just as well off to do what I did with the one pictured above: build your own rear control arms and use Miata uprights and diff. That is a MAJOR undertaking. Not impossible but not a weekend project either.
