Can't update my Nuvi 2597LMT, won't go into update mode

I reckon then that you must have a faulty socket on your nuvi since you've tried everything else I can think of. If so you could try installing the map to your PC using Express and then send the map to a sd card using a sd card reader or similar. Having done so insert the card into your nuvi as it can read it from there.

You might also try checking there is no dirt in the port in case that is the issue.

Longshot, but if you have a USB hub, perhaps give it a try.  There are several cases on this forum where that resolved an issue.  One instance where one of two Garmins was not recognized but a hub resolved the problem, can be found at device not recognized.  There is another case where a GPS would only be recognized with an HP laptop by using a powered hub.  That individual tried his GPS on several HP's at a Best Buy, all failed to recognize.  With other brands, no issues.

Yeah, that's what I was assuming at first, that my USB socket is broken. But then someone told me about the debug screen that shows the status of the USB port, and that it tells you if it's using the port as a recharge-port or a data port... and when I tried it I was surprised to see that it was being recognized as data: 

Furthermore, after I entered this screen the GPS for some reason no longer gave me that "This cable cannot be used for traffic" error message anymore even through multiple reboots.

I also tried cleaning the port and cable with Deoxit as one of the first things I attempted, it didn't help.

Can I use a SD card to install any other updates? Updates to the software, traffic, and other things other than maps? Then I was updating the 2595 on top of the maps there was six other things to update.

I don't thing I have a hub, I had some ages ago, no idea where they are. Though the software specifically mentioned to not use a hub.

Unfortunately you can send a map to a sd card and the GPS will read it, but software updates etc need to be installed on the device. It may be worth a call to Product Support as they may be able to help further.

I see, that's unfortunate. Will putting the maps on the SDcard "install" them in the same way that they would get installed from Gamin Express? (I know that it would apparently still put some of them on the SDcard due to the size of modern maps) or do they get loaded completely differently? How would I even go about doing that?

You need to use Express to install the map to your PC then BaseCamp or MapInstall to send it to the card. This assumes Express already has your GPS details in it. Note your GPS doesn't need to be attached to your PC to enable Express to send the map to your PC. 

If Express doesn't have your GPS in its list already then that's a problem. In which case have you ever backed up your GPS to your PC? If so there is another way to resolve it.

I only have the GPS settings for the 2595 on the PC, not the 2597

Did you ever do the steps to add the 2597 as a device?  See Add device