We had a similar situation. We bought our house a couple years ago, and went under contract in May for a September closing. The sellers were building their new home, and didn't want to move out until the new one was ready.

All of our time lines were standard (inspection, mortgage approval, etc.), we just spent a lot of extra time hanging out and waiting in between approval and closing. Since our mortgage commitment was only good for 60 days, we had to redo it several times. Rates were going up that summer, so we did suffer a fraction of a percentage point for it. It was a PITA, but we wanted the house.

One option that I haven't seen suggested is that you could close in a standard time frame, and then rent the house back to your sellers until June. We opted not to for a variety of reasons, but it can work. If you do it, make sure you have a full lease agreement drawn up, with everything spelled out to protect you. Talk to your attorney about it before taking any steps, and if you do it, have your attorney draw up the lease. One thing to be aware of is that some homeowners' insurance policies require the house to be owner-occupied, so you'll want to check on that too.

Given how much harder and more rigorous the financing process is now than in 2008 when we bought (we experienced it in 2010 when we refi'ed), I'd probably look harder at this option were we doing it now, just to get the deal closed.