I'm not sure you can BRG Hyatt's own website...

IME, I haven't seen changing rates on Hyatt site. I've booked separate reservations in a row rather than one long one (and used one diamond upgrade for both!). Obviously there is a risk that you may have to 'check-out' between the reservations, but if they're for the same room-type, you should be fine.

So if you can cancel without penalty, and the rates are for the same room-type, I would just book the 3 and 4 nights separately, and then cancel your original reservation.