You should use crimp ferrules on the wire ends for the terminal blocks that can be tightened securely then use one of the methods above to bond the sheath of the cable to the connector.

This sounds like what I was thinking must exist, I just didn't know what to call it. I'll definitely look more into this. Thanks!

 

I concur with Paul in post #8. You have the wrong type of connector. What you have is an interconnect between modules, designed for a secure and sturdy connection to allow dismantling for servicing a few times in its lifetime.

Depending on your situation, i.e. where is the mating end of that connector shown, you can replace the pair.
Or you can keep what you have and add another pair of connectors that are designed for repeated connect/disconnect, example DE-9P and DE-9S.

Sample photo:

The little green connector plugs into an Audio/Video switch, and the green connector comes with the A/V switch, so I don't have any option other than to use it... however, I hadn't thought of wiring a separate connection just before the green connector, which is meant for repeated disconnect/connecting.

For reference, below is the A/V switch that I ultimately plug into:

 

I've got the professional tool just for crimp ferrules but just about any cheap crimping tool works with a little practice.
http://www.banggood.com/0_25-6mm2-T...otlace-Ferrule-Crimper-AWG24-10-p-941280.html

Thanks for the video, this looks like what I was looking for!

 

Do a web search for "screw terminal connector strain relief"....
You'll find some things like this and you can ty-wrap the wire to the flange.

 

I like DJDave's solution.

Here's the thing: That connector is not meant to be plugged in and out on a regular basis. And wires that are not expected to flex will likely be brittle. In short, the wire is not meant to be handled on sharp angles, which is what appears to be the case with your connector. No doubt the strain relief will do wonders for your project, and I'm thinking you are not in a good position to completely redesign the switch box (change the connector).

In your mind's eye, look at a phone jack. Notice the wires directly enter the back end. That's the optimal direction for wires to be connected to connectors. Right angle connectors like the one you have are well suited for projects where wires internally may need to be disconnected for things such as programming or repair. They're mostly not expected to be plugged and unplugged on a regular basis.

To solve your problem - consider constructing some sort of strain relief that you can epoxy to the side of your connector. If you need right angle support - be creative.

Either find what suits your purpose or make something. But if you can, consider changing the sort of wire you're using. Use something better suited for daily handling like a telephone cord. The wires in those coils are designed to flex and flex and flex.