Edited on 2015-03-29 16:07:48
What about an engine from a Land Rover, it is a small aluminum 3.5 litre V8 _ the transmission that came with it is a 5 speed _ might be a bit over powered though...
That same engine and trans. was also use in the TR8 _ it was a Buick engine that British Leyland bought from them and modified it a bit here and there.

A better choice may be from a Mazda B2200 truck, which is actually made by Mitsubishi (with out checking).
Sweet little engine with a beautiful 5 speed tarns. _ it's machined so precisely there are no gaskets used in it's assembly.
I've driven many manual transmissions over the years (Rolls Royce too) and that one is very smooth.
The Mazda engine can be used with an after market Weber Carburetor as the original electronic carb is overly complex and there is no one around to service them anymore.
The later trucks were fuel injected, but that would require allot of modifying to get that system to work in your Triumph.

If you rebuild the old engine and have it balanced properly you will get a bit more horse power out of it. You can also raise the compression a bit by planing the head and/or adding material to the pistons to raise the compression.
You will need a better head gasket if you go this route, but I imagine a new head gasket will be made out of modern materials.
If you raise the compression by adding material to the tops of the pistons, the machine shop will have too compensate the weight difference on the crank shaft.
Valve clearance may also be an issue, but I am guessing that the Triumph engine has side valves, so clearance issues in that respect wouldn't be a problem.

If you put in a different engine, do you have someone to change the engine mounts, drive shaft length (maybe necessary) ?
Problems with the shifter position also have to be thought of, plus will the Triumph rad have the capacity to cool a modern engine _ a recore with modern matrix may be necessary.
A modern engine will require you to change the Triumph to negative ground to accommodate the starter and the electronic ignition on a newer engine.

That car was never meant to driven at 70mph on a freeway, why change it ?
It should be able to cruse at 50 anyway...

Lots to think about.