@FalkumelvaBob 

To ensure it is the modem, connect a PC via Ethernet to the modem bypassing the router and see if you have the issue.

Also be sure the modem/gateway is set in bridge mode.

  @ArcherC8 Thank you for your response!

When connected directly to the Cox modem via ethernet cable, bypassing the TP-Link, the network speed is excellent (500+ Mbps by Ookla).

However, during some experimentation, we encountered strange happenings.

Our other devices (smartphones, other laptops) that were still running through the TP-Link router at substantially reduced speeds quite suddenly and simultaneously had their normal fast speed restored after plugging one laptop directly into the Cox modem (bypassing the TP-Link) and using it for less than one minute. 

Furthermore, my wife, who is a Government Contractor and uses a VPN configuration for her Government-issued laptop, discovered the same phenomenon when she rebooted her Gov't laptop - all the devices that were slow returned to normal operation, again simultaneously.

Rebooting the TP Link also has the same effect of restoring all devices.

Other devices being rebooted had no local or global effect on improvement.  Also note that we have not observed the network healiing itself over time - it requires some sort of "kick" to start behaving again.

So, we think it is the network, and possibly the connection between the TP-Link at the Cox modem.  Perhaps a setting of one of the two boxes needs to be changed so that we don't experience the occasional slow-downs.

We're open to your speculations! 

Thanks again.

  @FalkumelvaBob 
few things...

Your Cox modem should be in 'Bridge mode' so it acts just as a modem and not also as a router.

VPN can slow down networks depending on the one used and how it is deployed.Since VPNs puts another devices in the stream of data it does have an impact on the data speed. If the VPN is just a direct VPN between your wife's company and her PC it should not be a factor. I would try at a time when her PC is not needed, to disconnect the VPN and power down her PC. This is to see

A

if the VPN and/or her PC is affecting the network. If you google "Cox and VPN" there appears others affected by it. Again this is a maybe, just something to check.

Sometimes other devices can cause slow downs. Selectively isolate devices by powering them down to see the affect on the network. For example an old printer may cause an issue or a PC having issues try to download data. Interference on a WIFI channel can be a cause. Interference can be caused by many different things not related to your network such as someone else's network or things like microwaves, garage door openers, security systems, wireless phones,... Try different channels and band widths in your WIFI settings. I like to use different SSIDs and passwords for each of the WIFI bands (2.4 and 5 GHz) as it allows me more control over the devices and where they connect. (do not hide the SSID). 

Remove and disconnect any unused devices from the network.

Uploading data (backups) to the cloud can put stress on a network.  

Ensure the cable going into the modem is clean and tight. If your Cox connection includes TV and such, check each of those connections at the TVs and any other connection points such as switches and splitters. Get rid of any dead drops where you may have removed a TV. Note if the problem occurs when you turn on a TV.

An Ethernet device or a connected USB device can slow a router down so isolating them needs to be done also. A router is just a small computer with very limited resources.

Review any logs the modem and router has and if anything appears to occur at the time of the start of the issue, check with the vendors to see what it means. The messages are not well documented for the end user.

If it appears not to be any devices causing the issue, and an extended test bypassing the router does not cause the issue, then I would try a factory reset on the router. That means you need to re-enter all your router settings.

Very rare, but your network may have been hacked. Change your SSIDs including the guest networks and the passwords using a long and strong password.

Let us know if you find something so it helps others.