Paul, when your headache is gone from reading all of this, try a new rotary switch. When a switch goes bad, it can pull the 24V down to ground internally since it is bolted to the meterbox
door. Your fuse is too big to protect your transformers, so get a four amp for the transformer. If your timer output is rated for less, go with that number instead. The reason your bill validators are cycling is that the voltage is being pulled down. Each time the motor cycles on the validator the amp draw pulls it even lower and the units 'loose power', and then the motor turns off, which makes the voltage go up a bit and the validator 'boots' up and cycles the motor again....repeat. If you have an ammeter, put it on the hot 24V line and have someone very slowly go through each function. Give a couple of minutes per function. If you see one that pulls a higher amount, the coil for that function may also be the issue (could be contactor, solenoid coil, relay, or whatever!) Another problem I have seen cause this is a
soap leak on a solenoid block.... The
soap is conductive enough to short from one terminal of a coil to another after the leak gets going enough...
Regarding the electrical talk, I might chime in that it doesn't matter what voltage or leg you wire a transformer too, the only important thing is that it is wired to the correct taps for the voltage coming in. A service with a wild leg (high leg delta) would require using a 240 V transformer or a multitap transformer wired to the 240V tap. A Wye service would use 208 Volt taps or a 208 volt transformer. If you used the 'wrong' tap or transformer, chances are you wouldn't have any problems, as the secondary (output) voltage would be off the 24V mark by up to 4 volts. Most electronics and loads would not have a problem with this.
Regarding grounding ouput voltage of a transformer, you can ground any single leg coming out of a transformer (you just can't ground two!). Since transformers are inductive, the secondary (output) is truly isolated from the incoming power, meaning that there is no reference to ground. Grounding any leg of the secondary makes that wire a 'neutral' wire because it no longer has a voltage reference to ground (it is grounded). However, the other leg becomes the 'hot' leg and will be a direct short if it comes in contact with ground.
Phasing in a bank of transformers is not important unless you are trying to balance loads for load distribution (not applicable in a car wash pumpstand). If you wish to make a 'common bus' along a bunch of solenoids that are each sourced from a different transformer, you can do that, but you can't forget to give the solenoid a reference back to its own transformer (you have to tye all of the commons together somewhere). If the transformers are out of phase with eachother, it will still work. Since transformers are 'isolated' individual circuits, the voltage is only in reference to its own source - not another source (other bays transformer) - even if one leg is grounded on each transformer. The only time you will ever have a problem is if some electronic device is truly using the ground to conduct its own internal electricity - which is a no no. A gfci would trip if an electronic device like this were hooked up to it...