Actually I read the HDB resale condition and it state somewhere that Buyer/Seller must not enter into any other agreement ... this include collecting rent or something like that.
So if you bring this up to HDB, they will not entertain your request for further extension of the 2nd appt, correct me if I'm wrong.
The only solution is .... check out the warehousing storage company like the one in IMM. You can rent for storing your furnitures and stuffs until you are ready to move into your new home. just google for "storage facility" and you can get a list of these companies.
Meantime you have to make arrangement for your family's accomodation with your relatives, parent, in-laws etc with a walk-in suitcase, if really desperate situation.
Hope that can help you.
Cheers,
Benjamin