Hi Matt
Lots of good advice coming in, but it seems you are not closer to diagnosing the issue. So , one step at a time so you can rule IN or OUT different fixes. Methodical will get the job done. Good luck.
Your comment above about flywheel spinning with little resistance shoots alarms bells for me . I may have feeble thumb and finger muscles but whether spark plugs are in or not i would expect spinning the flywheel to take some energy ( use of screwdriver lever as per Graeme). So I think it would be good to confirm
A) the flywheel and crank are firmly connected
B)the flywheel doesn't have any forward and back movement up and down the crank taper and it is properly bedded on the crank.
C) the crank is able to turn with the weight of rods pistons etc - so some resistance expected
If problems are as above then i think you will need to yank the motor to see what is going on.
( one thing to look for if you have to go this route - is the flywheel fully seating on the crank taper or is it being held off by slight swarf build up etc)
If the flywheel crank seems to be fine then a solution is likely NOT to involve pulling the motor - so small win there. As per a couple of suggestions from people above , I would look at:
Throw and then
Electrics ( you may choose electrics then throw)
I am not sure if you have measured the throw and the throw required ( i don't know if it is throw or pull on a verto) but the distance as Per Ethyl is important . On the Swarf photo it looks like one of the starters has been engaging about 2/3 of the teeth width ( as per Dusky) - maybe the old one ( some shinier wear marks to my eyes). BUT the noise on the video is very much starter not engaging the flywheel and I agree it seems as if the clicking noise is the solenoid returning once power is stopped - so either not throwing out the required distance or maybe not sliding into the ring gear and so pushing against the ring gear or maybe misaligned when energised ( i had a new pre verto type starter that had plastic like guides for when the bendix moved - this was cracked and flexed so the shaft when projected would be pushed to the side slightly
It would seem unusual for 2 different starter motors to behave like this - but if you have unknowingly changed the required throw out distance - then they both will struggle to engage the flywheel -the solution for this ( as I see it) is measure accurately the throw out distance and modify the starter motor to suit that length
This comment is for Graeme C or other clever wiring folks ( so don't rush in Matt)
Hi Graeme , is there any worth in bypassing the one or two solenoids in a row to see if something is getting diluted in translation? - so undo the bypass (or use the wing solenoid) AND add/ensure a good earth
Good hunting and speedy solution