Saints Cap Moves: Derek Carr restructured, Erik McCoy restructured; J. Williams released; cap space is at -$8,543,537

Eh? If they wanted to remove the no trade clause, Carr would have to agree to it. How does that make sense?
That's my point. Loomis said there were things to work on with his contract. That just means things that require both parties to agree to. A pay cut is just one of the things that both parties would have to agree to, so Loomis may have been referring to things that weren't pay cuts.

Also, you can’t change the length of a contract after it’s been signed and removing guaranteed income is literally a paycut.
Can't both parties agree to a new contract to replace the old one? Maybe the NFL doesn't allow that but it's commonly done outside the NFL.

You’ve, inadvertently, just said they were trying to agree to a pay cut, because everything else you listed is either impossible or illogical.
Everything I said is possible if both parties agree to it, unless the NFL doesn't allow renegotiating the length of the contract. The other things are renegotiable, but both parties would have to agree to it.

So, no, I didn't "inadvertently just say they were trying to agree to a pay cut." The fact is that Loomis could have been referring to things that aren't pay cuts.

I can not find a single quote from anyone in the Saints organization that they were asking Carr to take a pay cut.