Hi,
Sounds very similar to the issue I have had on my late bay & on my fastback.
The late bay was my fault (not sure about the fastback as it was like it when I bought it) as I accidentally let the (live) terminal that goes to the choke unit touch the case of the choke unit itself (ground) when I was messing with the carbs (remember kids, ALWAYS disconnect battery when messing about). Shorting this out fried the ignition switch.
The symptoms were that you had to just get the engine to 'catch' and then let go of the key quickly to get it to stay running - position 1 of the key was giving power to coil, but then on cranking, power was lost to the coil.
Quick check to see if yours is suffering the same problem - take the rotor arm out so it won't start - turn the ignition on to position 1 & get someone to check that there is 12V running to the + side of the coil. There should be. Then crank the engine and check that there is still 12V running to the coil - if there is not, there's your problem, ignition switch fried.
I changed the ignition switch myself - relatively straightforward job, just a little tricky - I did post up a 'tutorial' some time ago but not sure how to find it?
You can keep the same ignition barell & key, you just need to change the switch behind the barell.
hope that helps mate.