I recently switched from E* to D*, bought my equipment from American Satellite and received the 18" x 20" "Phase III" dish you are referring to.
The 4x4 multiswitch is indeed integrated with the three LNBs, with four outputs for connection of up to four receivers/tuners. You may have heard the integrated switch referred to as a "5x4" switch, but that is a bit misleading. There is no input for an OTA antenna on the integrated switch.
In order to hook up more than four receivers/tuners you need a multiswitch capable of passing/generating the 22kh tones necessary for the LNBs to work properly. One such switch (the one I bought) is the Eagle Aspen 5x8 S-4180-GX+. If you go this route make sure you buy the "+" model, as Aspen also makes an S-4180-GX which WILL NOT work. American Satellite has the "+" model in stock.
I believe the only other company that currently makes a cascadable multiswitch compatible with the "Phase III" integrated switch is Spaun. While Spaun makes an excellent product they seem to be about twice the price of the Eagle Aspen model. Terk is supposed to be releasing their own cascadable switch "soon", but I haven't heard any specific timeframe.
You didn't ask, but FWIW this was an extremely easy dish to point, much easier than the DISH500 dish I had with E*. Seems the smaller dish may be more focused, and the integrated LNBs make it virtually impossible to misalign.
As for a vendor, my only experience with DirecTV equipment has been with American Satellite and I had no problems. (well, none that weren't corrected promptly) Their pricing seems to be in line with what other online dealers are offering for new subscribers.
Good luck with your new system.