either going to rake the front end or rebuild to factory specs.
... the difficulty with raking the standard Triumph frame is the steering head's a casting, with tubes pinned and brazed into it. You could take all that apart and bend tubes to hold the steering stem at a different angle?
... or rebuild to which factory specs.?
Your bike's stanchions are aftermarket (longer than standard) and intended at the earliest for a '71-on Triumph or BSA; if they aren't tapered into the top yoke, the yoke's been modified and the stanchions are still aftermarket but intended for a disc-braked Triumph.
If the stanchions aren't tapered into the top yoke, you can give yourself an idea of whether standard forks will work with the hardtail - slide the yokes down the stanchions 'til the bottom yoke's about 6" to 6-1/2" above the black dust covers (over the tops of the chromed seal holders screwed on to the sliders). That's about the distance between the bottom yoke and the tops of the seal holders on standard forks, although the standard springs are outside the stanchions in that gap but covered with rubber gaiters. If the stanchions are tapered into the top yoke, you can still give yourself an idea of whether standard forks will work with the hardtail but you'll need to remove the top yoke and slide just the bottom yoke down the standchions?
Horizontal distance between the centres of the two fork legs will tell you the age of the yokes - 6-1/2" is pre-'68, 6-3/4" is '68-on drum-brake; there are also disc-brake but your bike doesn't have them.
If the fork sliders on the bike at present are the same '65 as the engine (and frame?), the suspension internals are very crude - one-way damping ... also the SLS front brake wasn't great 57 years ago, 57 years later ...?
'68-on, Triumph made incremental improvements to the front end, many of which are backward-compatible - '68 TLS front brake, different suspension internals including two-way damping; '69 moved the legs 1/4"(!) further apart and changed the TLS brake plate, changed threadforms from British Standard to Unified; '71 changed the triples and 650 twins to 'Ceriani-lookalike' - internal springs, exposed stanchions, ally sliders, those black dust covers over the tops of the sliders; '71 they also changed the triples and 650 twins to the notorious 'conical hub' brakes ... '73 they changed them to front disc brake and, although the forks look similar to '71/'72 conical-hub, almost nothing's interchangeable. As a matter of possible interest, if you collect all the relevant bits, a Triumph disc-brake front-end fits straight into your bike's frame steering head ...
fitted '95 Honda VFR forks to a T140D he sold recently - My T140 in the UK