The only thing to keep in mind about "borrowing" someone's HBO GO information is that HBO GO Terms of Services does forbid you from sharing the account with another person, so they could dump you for it.
Funny thing is that the HBO CEO says they know when you're sharing your HBO GO information and he doesn't care:
http://www.allvoices.com/contributed-news/16376813-hbo-go-knows-youre-sharing-passwords-doesnt-care
If you keep with Hulu Plus, Netflix and Amazon Prime, you should be good for most of the main items, if you don't mind them in some sense of delay. iTunes might be needed once in a while for things that end up there first for some amount of time, though that's pretty few and far between.
If you're on FIOS, you should have no issue with a high-enough speed for streaming, though the upstream speeds might suffer a bit.
I also echo the suggestion of talking to Verizon, asking for their retention department, explain the situation and see what they can do for you. You might be surprised about how much they want to keep you as a customer, either way.
Relying on Aereo for local TV might be a short-term thing, depending on how their case going to the Supreme Court works out for them. You could just get a HDTV antenna for the TVs that you'd want to watch local channels on and skip relying on Aereo.
I have Charter's 30/3 package (only one they offer), which has never been an issue for streaming, though it overprovisions so I get more than 30MBps downstream.