I can't compare between the Sony HX1 and your current H7 but I did play around the the pano in the store on the HX1 and thought it was a great way to accomplish that picture. It seemed to do a very good job albeit I didn't download the photo.
If you go the DSLR route each of the major brands has very nice entry level cameras and you can't really go wrong with any of them as far as quality and the ability to take very nice pictures. But there is of course a difference between a P&S with zoom and many auto scenes and using a DSLR.
I think each manufacturer (Sony, Pentax, Olympus, Canon, Nikon) has a package below $700. Sony has two new models that with rebates you could get a two lens package for around your budget or less or with a single lens they are both under your budget. Those are the A230 or the A330 with the main difference being that the A330 has an articulating view screen and live view. You might still run across the A200 or A300 which were the previous models and be able to get a good discount.