Alternator Replacement

a stronger 60amp alternator, or will it start frying the rest of my electrical system
The alternator's max output is only indirectly relevant.
1. The alternator only delivers what is demanded by the equipment. You can put a '60 amp' alternator on and if the only power needs are the ignition coil and alternator field (about 5 amps at 14 Volts), then that's all it will put out.

2. In many cases, and this would seem to be one of them, the important thing is to use an alternator that puts out enough power at idle speed to cover all the needs. Some higher output alternators are also better performers at idle speed. This would be what is you want if the amp is drawing more than nominal power anytime the engine is idling.