While I'm at it, I have another question.

Is there an easy way to use one camera for both computers using one of the USB ports on the monitors? Right now I'm using a Logi Brio and a Logi 920 camera, but I'd prefer to only use the Brio as it is a far better camera. 

Right nowm, the Brio is connected to the Optiplex and the 920 is connected to the WD19.

I'm also using two speakers UFOs wired to the Opti and the WD19. Ideally, I'd like to get rid of one of the speakers.

The keyboard/mouse is easy - the MX Master is connected via dongle to the Opti and via BT to my laptop that's connected to the WD19. It would be nice to be able to connect both computers using the dongle so that I could use one of my other laptops with the WD19, but that is asking alot.

Thanks all.

@redxps630 Wow. Outstanding. 

When we bought the 3080, we added a second HDMI because I was using two no-name monitors that only had one HDMI port each and was using my work laptop with a single old 19" VGA monitor with an equally old TB18 (or was it WD18? I get confused at Dell designations) that had a VGA output.

Dumping the WD19TB would be nice, but that is where the camera, Jabra 750 speakerphone (aka UFO) and the ethernet cable are plugged in. Is there a reason why I can't connect the dock via USB-C?

The more I think about it, I don't see a way for me to connect one of the Jabras, one camera and the keyboard dongle and have them work with both computers as I can't imagine that I could connect each computer via USB-C without thoroughly confusing the system.

At what point do I accept your solution as "the" solution?

You can keep the WD19TB dock.  It has a built in permanent usb c cable to connect to laptop. Then connect dock usb c w DP (#4 on dock) out to P2720DC #1 usb-c. The rest is unchanged from 1st reply.

3080 connects straight to P2720DC#1 DP in and has no business w dock or devices plugged into it.

If you like the answer you can accept as solution.

Great solution, but I'm not happy with Dell right now. I just got the two P2720DC's via UPS two days ago and was hooking them up today. They were both refurbished and while both had DP and USB-C cables, neither had a power cord.

While both boxes were a bit banged up, one of the two (let's call it #1) came without a sleeve over the screen and the base was quite dirty. It cleaned up nicely, but still.

The bigger problem is that the DP connection is intermittent. I'm going to swap monitors and cables to see if that resolves the issue. More later.

It is nice to have far fewer cables and the monitors are quite nice. Thanks for all your help.

For the life of me I don't know why the photo is sideways, but I think you can see another problem with this monitor - it has a nice little triangle of green in the lower left hand corner. Sigh. 

That one computer clearly hadn't been quality controlled before they sent it out - probably the reason for the defective DP port and the reason it wasn't even wrapped. Sheesh.

Did you get these refurbished monitors from Dell outlet?  I would return them if the defect was not described.

Yes, they were refurbished. Decent price on Black Friday. The description said that they were "like new" and included all of the cables. 

I've already opened a claim to replace the one monitor, so we'll see what they say on Monday

Dell customer service says that there aren't any more of these monitors - yet there are still several available on the site. I ordered a replacement and they are going to send me a label to return the damaged one - so all is well.

Now back to regular programming....

Earlier, I asked about how to best share peripherals between the two computers and I had a thought that I'd like to run by you.

The 3080 is connected DP to DP on monitor 1. The WD19 TB dock is connected via the USB-C to the USB-C on monitor 1. DP out from Monitor 1 goes to DP in on Monitor 2 - thank you @redxps630 .

Now, I'm left with 2 USB 3.0 ports on the side of each monitor and 2 USB 2.0 ports on the bottom.

Those ports can only be "live" when the monitor is connected to the applicable computer - so when the monitor is switched to DP, then the USB-Ports are like USB ports connected to the 3080. Equally, when switched to the USB-C input, the ports will act as if they are attached to the WD19 dock.

If that is correct, then I should be able to connect the shared peripherals to the monitors and have them switch along with the monitor's inputs - so I'd attach the camera, speakerphone, keyboard and so forth to the monitors - does that make sense?

The only thing that might be wonky is the mouse/keyboard because that wakes the computers - but I can just plug the Logi dongle into the 3080 and connect the laptop via BT - or maybe the other way around.

Am I thinking about this correctly? And does it matter which ports I use and on which monitor - as I think that everything is fine on a 2.0 port?

Re: Those ports can only be "live" when the monitor is connected to the applicable computer - so when the monitor is switched to DP, then the USB-Ports are like USB ports connected to the 3080.

I am not sure. in my experience the monitor USB ports become live when the monitor is connected to pc via a usb upstream cable (typically usb type B on monitor end and type A on pc end).  Without such cable, at least my professional ASUS monitor USB ports are not live: they do not charge my Bluetooth headset device for instance.  Now maybe your dell monitors are more modern and use some technology that I am not aware of.  I just do not know whether the single DP connection bth 3080 n monitor is enough to turn monitor USB ports live.  I think not, but I you can prove me wrong if you test it.

@redxps630 - sadly, you appear to be correct. If I connect the camera, and speakerphone to the USB ports on the first monitor, then they work with the computer that is connected to the WD19 that is connected to the USB-C port on the first monitor, but they stop working when switched to the DP input.

What I haven't tried is going with a USB-C cable from the 3080 to the monitor to see if that turns the ports on. I'll try that on the weekend.

Although a bit late, I thought I'd come back with a bit of an update. 

I could never get the ports to work reliably with both computers, so I bought a cheap peripheral switch on Amazon. That worked but was awfully glitchy. The included ASB-A to USB-A cables were junk and I could not rely on anything to work. But, because it kind-of worked, I decided to buy a better peripheral switch and found the IOGEAR GUS432 that seems to be better quality and, to date, has worked reliably.

The peripherals (mouse/keyboard dongle, camera, speakerphone and headset) are plugged into the IOGEAR and that, in turn, is plugged into the Optiplex and the WD19. The IOGEAR comes with a wired remote that you press to switch between computers.

Press the button on the remote and, while that is switching, change the input on the "main" monitor (the one that the Optiplex and the WD19 are plugged into) to whichever input you want - the other monitor will switch by itself.

Now for the next project. I just bought a MDS19 dual monitor stand and a couple of MK15 docking station mounts. I'll see if I can attach the OptiPlex to one of the mounts using the Optiplex VESA mounting bracket and the WD19 to the other monitor to get everything off the desk - or should I scrap that plan and just put the OptiPlex on the monitor base on one side and the WD19 on the other side?

TL:DR

Two Dell P2720DC monitors

One OptiPlex 3080 Micro and one WD19 docking station connected to my laptop.

Four connected peripherals - mouse/keyboard dongle, speakerphone, camera and the dongle for the headset - via a peripheral switch.

The OptiPlex is connected to the first monitor via a DP cable. The docking station is connected via USB-C cable.

The second monitor is connected to the first via DP-DP cable.

I can switch between computers easily and use the same peripherals and everything works as intended.