Tiny voltage spikes from the 30v line heading back into the transformer and likely creating an issue through ground. (the bonus lights don't even have a connection that's NOT ground when the rotating disc unit isn't on them so) An LED is either on or off while an incandescent light bulb's brightness is dependent on voltage, so these tiny little spikes don't light an incandescent bulb up enough to where it is remotely visible.
Are your bulbs good quality? Where did you get them? I'm surprised their tolerance is that high to where they would light with not much voltage.
You can fix this by purchasing a 6v transformer online assuming your lighting has a separate ground connection from the solenoid line (even if they are tied together at the transformer) that can be removed and added to the new transformer. Make sure it has a rating of or higher of the fuse rating for each part, actually, the LEDs will draw a lot less power so you'd have to measure what each is sucking - may be better to run them off of separate transformers if you can't find one which accounts for enough - remember to account for the insert lights which are not lit.
If your LEDs drop the usage below 2A you can just use something like this, but MAKE SURE to remove it before selling it incase the next buyer uses regular bulbs. (Incase it burns up)
ebay.com link » 6v 2a Power Supply Adapter Charger Ac Dc Transformer 5 5mm X 2 1 2 5mm
At the same time it would be a good idea to lower the fuse rating in the playfield and backbox fuse holders based on your findings when measuring the amps they draw, because as stated, the LEDs would draw significantly less.