Sounds to me like your alternator is not up to the task. If you can't start the engine with the spotties on, then it's battery or wiring.

It could be a bad earth on the 12V feed to the high beams, possibly a bad relay.. But an ammeter inline with the 12V feed to the battery side of the relay (Which I expect you have for these spotties) will tell you the story. With the engine running and the high beams on, does any of your wiring get hot or even warm? They shouldn't even get warm, if they do, look for a bad earth or get thicker wire..

Chris.

ps. Make sure that your ammeter can cope with 20A + otherwise you'll cook your ammeter. I've done it, it doesn't look or smell nice.