Uh Lonewolf, the Warrior is a bucking bronco of a linear. If it doesn't throw you now and again, something's wrong.
What you are seeing is instability inside the linear. The "SWR" you are seeing is not really 'swr' in the normal sense.
The Warrior is pumping out extra frequencies. Maybe harmonics, multiples of your channel frequency. Maybe just "oddball" frequencies. What the SWR meter is telling you is that RF at a frequency WAY off of your channel is coming out of the Warrior. It's stronger when only a carrier is coming out, and becomes weaker when you modulate. Not an unusual bad habit for that model.
The SWR meter can't tell how many different frequencies are coming out of the amplifier. It just adds the sum total of the power they represent, and shows you a reading.
Trouble is, power at frequencies AWAY from the ones the antenna is built to accept will not be "soaked up" by the antenna. If you are (inadvertently) feeding 54, or 81, or 108 MHz into the antenna, it's not tuned for those. Nearly 100% of the power at those frequencies "bounces back", and makes the reflected side of the meter read really high. RF power that is spread across multiple frequencies will fool a SWR meter. Well, fool it in the sense that your SWR ON your channel is still low, even when the meter reads high. The clue here is that it changes with the amplifier's output level. And the other clue is the model.
Taming a Warrior that wants to be unstable is a by-gum and by-gosh process, even for a an experienced tech who has done it before. There is no published "step-by-step" to be found anywhere I know to look.
Ed DuLaney's design concept was used in models that had from 4 to 16 tubes. His 'formula' for desiging them ran out of steam at 12 tubes. Worked pretty effectively with 4, 8 or 10.
But 16 tubes was pushing the envelope for his basic layout method. Four driving four driving twelve is just too much gain to cram into one cabinet. The result is that the Warrior will act crazy, more likely than not. Quite often, you'll find that the bogus "SWR" reading falls off when one of the (three) plate-tune controls is cracked just one side or the other from its peak position. Or maybe not. That's the basic sort of instability I've come to expect from that one.
It's not out of reason to find that the Warrior will behave differently with one antenna than with another. Doesn't mean that either antenna is not a good design. What you are seeing is the way different antennas behave at frequencies WELL AWAY from the 11-meter band they're DESIGNED to be used on. An amplifier that is THIS choosy about your choice of antenna is,... well... not stable.
Sorry I can't offer some more constructive advice, or specific suggestions to tame it. Removing the four-tube "predrive" stage, and feeding the drive directly to the next 4-tube stage will make it into a 12-tube Phantom, sorta. One with an oversized power supply. That's the most effective answer to this problem that I have ever found. Doesn't get an enthusiastic reception, usually. People fall crazy in love with the idea of using all sixteen tubes. Never mind that it will work better with twelve. That's the problem with falling in love. Makes you do stuff that's objectively crazy.
Umm. P.S. I tend to ignore antenna discussions. Never mind why.
73