RE the top pics- they are not in correct alignment. The idler gear needs to be lifted up and re-placed so that the marking with identical length dashes is lined up with the crankshaft gear dot. This will place the long dash/short dash at the inlet gear, and the dot to match the dot on the exhaust gear.
On 5T models, the inlet gear would align with the short dash, and on the TR5, it would align with the long dash.
There is a difference to permit the opening of the cam a bit earlier on the sportier model, should run with either dash aligned, but should run better with the right one aligned, and would run best if you can properly time the camshaft opening to it's best position following the valve timing instructions in some of the old pre unit manuals
Sorry, can't answer the why part on the differences-too many years, models, and gears..........
Pullers- a nice set for pulling can be found at almost any good Brit bike dealer- also check E-bay, especially if you are going to do more Triumphs in the future.
P.S. I hope that's not the wife's coffee table that engine is on. Could prove to be fatal!!!