24mm is ultra-wide but you are right, there are now a few cameras with 22.xmm lens which is slightly wider. You also want to use an add-on flash, so what you are looking for is a ultra-wide-angle camera with a hot-shoe.
As you can see from the search link, there are 12 such models, you will have to see which one fits your budget. The Fuji X-S1 is probably your best bet and delivers good image quality compared to its peers. It also looks really professional since its as big as a DSLR.
As was pointed out, the X-S1 is slightly above your budget. The model just below it which also has a beautiful 24mm ultra-wide mechanical lens is the Fuji HS30 EXR. It does accept conversion 58mm filters (or bigger via a step-up ring) too if you want to go wider without stitching.
The other option is to go to the used market and get yourself a DSLR and ultra-wide or fisheye lens. Any will do for your purpose, so it is more of a matter of availability and at what price you will find one.