Oh gosh, I feel your pain and have been in this situation. How I handled it was push it all back to the person who's responsible for it. I've never had anyone get upset or mad because I wasn't willing to pay for business expenses out of my pocket.
This was what happened with us: Even after receiving shut off notices, the correct billing still wasn't addressed and the bill(s) went unpaid. The electricity was cut off to an employee's apartment, I was at the brink of calling the utility company myself and decided I wasn't going to take this on. No one in the apartment was on a lung machine, it wasn't dead of winter, etc. When I learned of what happened, it wasn't during business hours either so getting hold of someone wasn't too easy. But I did get hold of someone who called the utility immediately and made the payment. The second time the power to the property (laundry rooms, lights) was cut off. There was no way I was going to cover a several hundred dollar electric bill.
Although I hope it doesn't go that far, keep in mind that it takes minutes, not hours or days for services to be restored. It's not always necessary to be brutally honest, you can tell the tenant(s) there was a glitch and services will be restored shortly.
I know this will eat you up, but you just can't carry the whole load yourself. You've made them aware of the situation and it's now up to them.
As far as your vendors, all of them have experienced a payment delay or two without cutting off services. However, if they require immediate payment this is another bargaining tool for you - can't complete turns for move in if the vendors aren't paid.
If the owners ask you to cover expenses yourself, it's OK to tell them no. On many occasions when expenses have come up and that questioning silence followed, I made sure to say I'll need a check for expenses, they'll need to put the purchase on the credit card for me to get the material, etc. Tell them that you've not in a position to take money out of your pocket or put expenses on your credit card. If you start paying for things yourself, you're already telling them that it's OK to take advantage. Do know though that there are times when I do make purchases when I'm out of petty cash but it's for small things that won't affect me.
When the owner or whoever starts getting the calls about power shut offs or you tell them you can't send them what they need or process rents or get turns done for move ins, I guarantee you things will start happening.
Hopefully it's a situation of they've just haven't got to it yet but it's on the list. Good luck.