Old equipment

You obviously have an older account. The D11's were discontinued long ago and don't even support HiDef channels. I'm also guessing that you do not have a modern Single Wire Multiswitch dish because the D11's don't support that. 

How many TVs do you use?

Your best upgrade option would be to get a Genie DVR (HR54) and potentially keep the 2 HR24 DVRs. You might also need one additional Genie Mini Client to replace one of the D11 boxes. That would give you the ability to record up to 9 channels simultaneously. And, with a modern SWM setup, your HR24s can link with the HR54 Genie so you can view any recording on any DVR.

Sadly, that's not the upgrade that DirecTV will want to sell you. They'll want to push the HS17 Genie Server and Genie Mini Clients. That would require you to dump your HR24s since the HS17 only supports Mini Clients. 

First, each HR24 has only two tuners so you can't record two channels and watch a third on each DVR. 

Second your D11s are very old and will only receive SD signals, and Directv is moving to remove all SD channels so at that point your D11s won't work at all. So you certainly need an update.

Your best bet is probably to get your D11s replaced by Directv under their free MPEG-2 replacement program. They will probably replace them with H24 or H25 receivers. This is a swap NOT an upgrade (don't use that word). Swaps are free, upgrades are NOT.

They will probably offer to replace all your equipment with some model of the genie server plus three client boxes. If it's an Hr44 or Hr54 that will have only five tuner shared between the four boxes, The clients don't have their own tuners, all the tuners are in the genie. If your existing setup is spread between locations (such as having a receiver in an RV) the Genie solution WILL NOT WORK because the clients have to be in the same location as the server.

My suggestion would be to call Directv and discuss the swap program and see what they offer you. Then get back to this forum to discuss before committing.

Are the response time issues on all the boxes or just some, if so which? 

You actually have the newest non genie HR model DVRs. I still have an HR-22 and yeah, it can take very long to change channels too. Those models only have 2 tuners, that’s why you can only record 2 channels at a time but since you have two DVR’s, you can record 4 channels at a time. You can, of course, record two channels and watch a recording at the same time but you can’t record two channels and watch a live channel. If that just doesn’t meet your needs or the slow response is too much, the only upgrade available is a genie and if you get the newest genie, the HS-17, you will have to replace the HR-24’s and even that has been around 4-5 years. I’m not familiar with the d-11, not sure if you can keep them or not.

The HR24s are the last receivers made before the Genie line came out and are still a great model, you can try to get warranty replacements.  The D11 are obsolete when DTV finishes their MPEG2 channels shut down so need to be replaced with HRXX with their free swap offer that will replace the dish if needed to a SWM dish. The only other route is with an HS17Genie2 and lose all the HR24 and D11 for minis.

You never could watch/record 3 live programs at the same time, only record 2 and watch a recorded program.

@wadestvs 

You have MPEG-2/SD-only boxes in the mix that use the older multiswitch. You are definitely in need of an upgrade, not just because of your performance and tuner concerns, but that MPEG-2 feeds are shutting down.

HDDVRs have 2 tuners. So when recording you are tuned into 2 channels so cannot watch a 3rd. The D11s are very old and must be replaced as those are the MPEG-2 boxes.

Order a Genie, which should get you either the HR44 or HR54. Make sure the order includes one Mini Genie Client, no more. This is just the replace the D11s as your HR24s work with the Genie.

The Genie is a 5 tuner HDDVR. It shares those tuners with the Mini Genie Client. As the D11s have 1 tuner each, you gain 3 total over what you have. Naturally have the Genie end up on whichever TV needs the additional tuners. It also has a 1TB hard drive (double the space of an HR24).

Make sure you do NOT get a Genie-2 (HS17) or that would replace all your boxes which would be a downgrade as every TV shares it.

Genie comes with Whole Home DVR ($3 monthly) allowing each HDDVR (and the Mini Genie) to watch what is recorded on the others.

With an updated multiswitch, along with repairing/replacing any bad connections they find, that may see a small boost in performance. The increased tuners will help when you want to watch another channel when 2 are recording already.

As a side note, if any of your TVs are 4K you could mention that to ensure the Mini Genie is the C61K (goes on the 4K TV) and the main Genie is the HR54. Only do this if you have a 4K TV as tech should refuse install otherwise. There is no cost for 4K, just needs those models at minimum.