Audioquest XLR cables are overly tight/stuck in equipment sockets. Advice

"a pain in every piece of equipment I’ve used them in"

I think I would purposely destroy the end of the cable at the connector, and somehow get it out and throw them out, or put new connectors on if the cable is special rather than take the amp apart.

I like that most XLR connectors lock, and it doesn't hurt to get a slightly higher signal strength than RCA, but at home we don't need the 'best' shielding that pro installs do.

I have had good luck with Locking RCA connectors, even these relatively inexpensive ones from Parts Express

https://www.parts-express.com/Locking-RCA-Plug-Solder-Type-2-Pair-091-1270?quantity=1

I haven't had experience with these Audioquest cables, but it has always been my premise that the connectors on cables are their weak point. My view is the tighter the better.

". . . purposely destroy the end of the cable at the connector. . . "

A really bad idea.  

- - - 

Both male & female XLR connectors are enclosed by their casings.   Opening up the amp will not help.  Look at this photo.

There is a solution:  

• Contract the XLR connector on the cable side with cold – such cold air or ice.
• Expand the XLR connector on the amp side with heat – such as a hair dryer.

Disconnect the amp from power.

• Use a hair dryer to blow hot air on to the rear panel of the amp by the XLR connectors.

Try to avoid blowing the hot air on to the XLR connector on the cable side.

Feel the heat differential with your fingers.

• Turn a container of canned air (Dust-Off) completely upside down.
• Very cold air will stream out.
•  Aim the nozzle on to the XLR connector on the cable side.  Chill the connector for about 5-10 seconds.
• Try your best to avoid chilling the XLR on the amp side.
• Practice your aim with a spurt or two.
• Within seconds, start wiggling the XLR connector out – carefully.
• Do not grab the cable – only the XLR connector.
• The XLR connector will be very cold. You might need a lightweight glove.

 Warning:  Turning the canned air upside down will empty the container very quickly. So be frugal and/or have a couple of cans available.  Practice your aim first.

In addition:

• Sparingly insert just a couple of drops of very light-weight oil – such as sewing machine oil around the XLR connector on the cable side.   ONLY A COUPLE OF DROPS!
• Since the electrical connections are enclosed in the casings, the oil should never touch the electrical contacts - only the exterior casings of the connectors.
• The light oil combined with the cold air should do the trick. 
• Skip this oil application if you’re not handy.

Good luck!

If you think the problem is just the spring-loaded latch, try sticking jeweler’s screwdriver into the latch.   Or something thin.   Be careful.

Try to determine if the connection is tight on the well or the conductors too tight on the pins. If it is the pins, send them into Audioquest and they should repair or replace them. But first follow steakster’s advice, very well explained procedure.