Under the circumstances it sounds like you handled it the best way possible.

In that circumstance, special rules under IRC Sec. 732(c) will apply.For property received in a nontaxable distribution, a partner's holding period includes the partnership's holding period [IRC Secs. 735(b) and 1223(2)].This is a complicated issue. 

When you call each hard money lender, ask them what will they do if you have trouble pay back the money under extreme circumstances, e.g. lost your job.

I'm sympathetic that it's not financially or physically possible for you to do that but, at the end of the day, no one else is responsible for those circumstances either. 

I know for a primary residence you need to live there for a minimum of a year unless there are some sort of special circumstances, is this true for a rental?

A lot of factors are creating some very unusual circumstances.

There are occasions where, in the future (but less than 12 months) if something changes your circumstances (such as getting a new job that you can't commute to) then you can probably get away with moving, because your "intent" at the time of the refinance was authentic. 

We were originally told they were doing cash for keys, which made sense considering the circumstances.

However there has to be a legitimate change of circumstance for change.

A smaller local bank or credit union would be more likely to fund under these circumstances.