Push the engine compartment wires out from under the dash; separate the bundle (from your temporary taping to pass them through the grommet/hole) into the wiring on the LH/RH sides of the engine compartment__the wires should flop/land very close to their connection terminals.
The only really hard part will be to secure the rear harness alongside the bellhousing, as there's just too little room with the trans in place (removing the trans cover may help some, but I'd settle for ty-wrapping the new harness to an old harness clamp until the next clutch job...).
Go ahead and remove all the old terminations, as the colors are likely so faded/grease or paint covered as to be of no help anyway. And again, the new wiring will land so close to where it terminates, that there should be little confusion.
STUDY the wiring diagram! BTW, you're not color-blind are you...?
Don't get overwhelmed thinking about the entire job, just concentrate on one (1) piece of equipment or gauge at a time.
Neatness counts! Try to avoid wires twisting over each other, and dress them out so that they flow from the harness bundle to the devices. In aircraft wiring, it is an absolute no-no for one (1) wire to lay across another, because if one (1) overheats and melts the insulation, it will short to the wire it crosses. It IS possible to manipulate the wiring inside the taped bundle to have them exit in an orderly fashion. It's not uncommon to undo a wire that's already terminated in order to make an adjacent wire look neater.
That's a start, good luck! If/when you get frustrated, walk away! When you return, it will all look clearer, and you'll be that much further ahead.
Oh, and be glad you're wiring a Healey, and not a modern BMW with miles of tiny wires, buss-communications and fibre-optics!