Almost done that.
Not on the SEM though, it was done on a 50 cc Victoria moped engine.
A transformer rated at 4W @ 50/60 Hz was (more than) enough! There was no regulator to bring the AC out of balance. The frequency was not as high as the sem will give in a husa engine. The discharge capacitor was only at 0.5 to 1uF and 400V. So it was easier to make it work. It even overcharged the capacitior and eventually it... Umm... Didn't I describe this previously? Wait a bit...
Here:
http://www.husaberg.org/index.php?na...t=2408&start=0
Diodes and especially bridges for 50/60 Hz are not optimal, the berg will produce up to 1000 Hz. The Victoria couldn't have produced much more than 100 Hz! Try fast diodes instead. Also, try to run it without the smoothing capacitors. The voltage from the original charger coil is far from smooth. Also, the regulated electric tension from the lighting coils is AC with overlayered DC which is something that transformers do NOT like, the DC part that is. DC will lead to magnetic saturation and excessive heat build up in what you use as the primary winding (which was originally intended as a secondary one). Either filter the DC out with a large bipolar capacitor or else get a symmetrical regulator.Then will perhaps your small transformer be more than enough in your case too.
Maybe could one lighting coil be used unregulated if a suitable inductor was connected in series to protect the discharge capacitor from too high voltages at high revs. But that would take some experimenting.
A 100 VA transformer for 50/60 Hz is a bit too large, if you can get an aircraft transformer, they are designed for 400 Hz and are much smaller for the same power.
Your trick with a transformer is definitely what I'll try as soon as the stator breaks. But it has been around for a number of years and it just won't quit. But when the day comes...
An inverter is an alternative. Especially if the bike has got a battery. Emco is one inverter brand that could be considered unless you want to design your own.
Good initiative with the transformer. Thats the way they should have been built from the beginning.
Regards