You are, in my opinion, skating on thin ice with this. Is this a machine safety issue, or a maintenance issue? If it is for machine safety, what you are doing is likely to get someone injured or worse. If it is strictly for maintenance purposes, and a full Lock-Out/Tag-Out power lockout routine will follow the big push button, then OK, but it doesn't sound like that.
As to your multi-contact buttons, what you are experiencing is the limitations of the physics involved in making push buttons work. Each set of contacts has an amount of force needed to not only separate them, but to push them together when you want them closed. So to make that happen consistently, contacts are "floating" on springs and the amount of movement of the actuator is absorbed by those springs. But with each contact set, there is a 'slop" in the movement and once you get too many stacked on top of each other, the cumulative slop results in the ones at the end not having enough movement to operate reliably.
That's why people use relays... If this is not a machine safety issue, then you can use what are called "mechanically latched" relays, they maintain their state regardless of whether power is available or not by virtue of having two coils, one that you energize to latch, another one that unlatches. Of course if there is a fire and power is lost, you can't operate the relays but then again, the machines would be powered down as well.
" We are all here on earth to help others; what on earth the others are here for I don't know." -- W. H. Auden