It needs to have a OTA tuner. Sometimes atmospheric conditions can interfere with satellite reception while OTA reception still works. We get probably 50 OTA channels, including the major networks. The 722 can record OTA at the same time as satellite.
While not internal, it can be purchased and attached to a USB port on the back out of sight. The modern ones are dual tuners, so two separate station recording alongside satellite recording is possible.
It needs to have component output in case I want to use one of my old projectors. I have a box that is supposed to enable recording HD from a component output to a computer. I just never got around to hooking it all up to try it.
Hopper 1, 2 and 3 all have component out, the Hopper Duo (being the "budget" model) has composite out only. The "Plus" versions of the Hopper2/3 are HDMI exclusive. Still have a slingbox (RIP) attached to one of my two Hopper3's.
It needs to have a analog uhf/or vhf output cus that feeds into a antenna distribution system so any tv anywhere in the house can display whatever is on the dish box.
An inexpensive modulator can be had for $10-20 bucks that connects to the composite output of a Hopper and transmits on channel 3/4, only issue here is that the component and composite outputs share audio jacks. You could get creative with splitters or use a Joey (second box or "head" to a Hopper system, has a monthly fee however) that also has composite outputs.
It needs to respond to the 722s uhf remotes that are near those other tvs all over the house.
If you want to use the same 20/21 model remotes via UHF that wont be possible, Hopper generation receivers can only use those remotes in IR mode. All Hopper remotes are UHF, so you could purchase the model 40.0 which has an identical layout to 20/21 remotes and spread those around the home instead.
Note: the SD analog picture is good enough for little bedroom tv's.
These will remain the same if you go with and RF modulator.
It needs to not have an increased monthly cost.
And here is the deal breaker, as there is no Hopper receiver with the same monthly cost as a 722. I'm guessing you are getting the 722 at $7 per month, so you could go for a Hopper Duo at $10, but it only has a composite out as previously mentioned and a rather short UHF remote range given the antenna is internal. You could also try your luck at getting a Hopper3 discounted from dish (IIRC new customers get $5 off making the monthly rate $10) but you are spinning the CSR roulette at that point.