I would not attempt to not feed for a week.
I would do an automatic timer as well, if you have no other options.

I am very concerned that they might turn off the heat/electricity while you are gone,
killing the frogs with very cold temps.

Can you go to a pet store and ask about paying them to frogsit?
If not that,
I would put an ad on Craigslist and find a local fish dork who could care for them.
Money talks, so offer a bit of $$$, and I bet you could find someone.