Owen,
I wonder if the isolator was defective and that is why a lead was taken off. Someone had to go out of their way with some good reason to remove a wire off of it. I think that is probably a separate issue but needs to be sorted out also.
Regarding the slide, either the relay is wired wrong, or the relay is not working at all and the slide circuit beyond the relay is getting an alternate source of 12V with the ignition on. I do not think the battery change had a whole lot to do with this, but it could be that if you had really bad batteries with a voltage level that was dragged well down, you may now have relays and circuits that are operating with the higher voltage that would not activate before. If that is the case, the outcome is still to finding the relay that feeds the slide circuit power and see what is happening with the ignition turned on and off. I expect that the relay is being activated by the ignition switch as it should and that the NO NC contacts sending power to the slide is wired wrong.....I know that makes little sense given that this use to work properly but the symptoms indicate that the relay is active coming from the ignition switch, just the wrong logic is being used. In my computer life you are getting a 1 when you should be getting a zero....
Later Ed