You will be able to connect three dual tuners to power 6 tvs with the 722, 522 and 322, however you will need a new dish installed or a wing dish depending on where you live and what equipment the installer has with him. Depending on which market you live in, you will either receive the 129 satellite for HD (this is the WA western arc) or the 61.5 satellite for HD (this is the new EA eastern arc).
If you live in the WA market, a dish 1000.2 will replace your dish 500. This dish receives 119, 110 and 129 and has three outputs and has a Dish Pro Plus LNB which allows for a single cable from the LNB to each dual tuner receiver with the DPP separator.
If you live in the EA market there are two options with the single dish solution being the best option. Again, the single dish solution will replace your dish 500 with a dish 1000.4 which receiver 77, 72.7 and 61.5. This dish is also DPP with three outputs similar to the 1000.2. The other option is installing a "wing dish" pointed at 61.5. Normally, this would connect to the LNB input of your existing dish 500 DPP LNB, however you would like to power three dual tuners which you would not be able to with that configuration. Instead, you would need to replace the DPP LNB on the dish 500 with a dish pro twin or quad LNB and install a DPP 44 switch. In that case two cables will need to be run from the 500 to the switch and a single cable from the 61.5 to the switch, then a single cable to each dual tuner receiver with DPP separators.
It can be somewhat complicated, especially if you haven't pointed a dish before or used the equipment. If you order the equipment through Dish, they will not send it with out having an installer set it up for you. If you purchase everything yourself, you will have to be comfortable setting everything up first.