Upgrade equipment, wireless, and expand number of concurrent viewers

The Genie (HR44 is the 2nd generation) is a 5 tuner HDDVR. It reserves 2 tuners to itself for Picture in Picture (PiP).

The C41/C51 are Mini Genies which are Clients, not receivers. No tuners or recording space of their own, instead each being an extension of the main Genie. Each Client uses 1 tuner.

That means Genie and 3 Clients at most can be in use at the same time. There are 4 Clients, meaning there is 1 more than capacity for simultaneous use.

H23 is an HD non-DVR receiver. Has 1 tuner of its own. It also has Autotune if it matters, a feature exclusive to non-DVR receivers.

Personally I would have replaced the Clients with HDDVRs over time to get 2 tuners and 500GB for each box. That would solve the concurrent viewing problem, increase storage space, and less TVs reliant on a single box to run them. Unfortunately DirecTV was pushed away from that after acquired from AT&T. Those HDDVRs (HR24 being last model) are still available through Authorized Retailers such as Solid Signal, but are more difficult to get someone at DirecTV to activate them.

Now your best option may be the Genie-2 (HS17).

The HS17 is a Headless Server tower. This doesn't go on a TV but functions as the Genie server for all the Clients. Has 7 tuners and a 2TB hard drive, compared to the total of 6 tuners and 1TB you have now.

This would allow all 6 TVs to be in use with a tuner left over for something recording.

Has a wireless video bridge (WVB) built-in to connect to any wireless Mini Genies (C41W and C61W), or Gemini (C71KW) that you have. The range is up to 80 feet under ideal conditions. Like the regular Genies, it does support an external WVB on the coax depending on your home's coverage needs.

Since it only allows Clients, and multiple Genie/Genie Lite/Genie-2 boxes do not work together, this would require replacing the HR44 and H23 at minimum. There is no PiP or Autotune with the newer setup. Recordings from the HR44 do not transfer so is suggested to be comfortably caught first.

A caution, this puts all eggs in one basket. So if something causes the main box to go down such as a technical issue, power cord pulled out or made loose by cat laying on it, etc. than all Clients go with it as they cannot work by themselves. If that were to happen to their current setup with the HR44, the H23 would still work as is a dedicated receiver.

So the Genie-2 is a moderately capable setup and built for a one-size-fits all (or at least simpler for the company side in my view) at the cost of some flexibility.

Monthly cost is the same if they keep the same number of TVs. Any equipment upgrade would come with a 24 month service agreement.

You seem to have it correct. To summarize:

To keep with 4 Clients and use them all at the same time, then the only option is the Genie-2 (HS17).

Both your HR44 and H23 would be replaced with Clients as the Genie-2 doesn't go on a TV. Recordings on the HR44 would be lost as they are encrypted to their exact box so cannot be transferred.

Putting the Genie-2 where the inconvenient drop is may work. The key part is the range of the built-in WVB is up to 80 feet under ideal conditions to where you have a wireless Client.

If it has been at least 2 years of active service with account in good standing since their last upgrade (adding a TV counts), then a free upgrade is normally available. That free upgrade usually covers one box, with the exception for more if it requires it (such as the Gene-2 only allows Clients meaning two boxes must be replaced).

Unknown if a wireless Client would be covered by that option. If not, then it would be the one-time lease cost of $99. Either way comes with a 24 month service agreement. The monthly bill should remain the same if you are not adding another TV.