The twin cam in my elan looks stock but it does have an Aldon ignitor hidden under the dizzy cap. Makes life a bit easier.
As a quick fix, try changing the rotor arm. I had one where the rivet on the top was too long and when it got hot it would allow the spark to "leak" straight through to earth onto the dizzy spindle. Took a while to figure out as it started intermittent as a lack of power at certain revs (that bogging down feeling) but when hot would just cut the engine. If you left the car to cool down for 30 mins it would start fine, up to the time it did not! A bit of research found there had been a quality problem with them, so I now carry a spare just in case.