...which leads me to think that the problem is only with the higher wattage provided by the amp.
SWR shouldn't change with power level. If it does, then it usually means one of three things:
(1) harmonic or other spurious output at a frequency where the antenna isn't matched
(2) the meter isn't accurate at one of the power levels (commonly they read low SWR when the power
is barely adequate to drive the meter to full scale.)
(3) something is arcing at the higher output level. It might be the end of the antenna wire, or a stray
strand of shield wire inside a connector. If this is the case you should see the SWR suddenly start
to jump around as you raise the power to a certain level, and it will often be erratic.
If you crank down the output power on the amp to match that from the transceiver and still see
the problem, it won't be (2) or (3).
If you are, in fact saying that none of the cables prior to the meter/antenna can affect SWR, then I really don't have a clue as to what is going on as I have not touched the antenna cable at all.
That is what I am saying - the meter reads the SWR on the antenna and coax past where it is inserted
in the feedline. Changes in the coax jumpers may affect the amount of power arriving at that point, but
not the SWR seen by the meter.
You may not have intentionally
wiggled the main coax feedline, but with most SWR meters I've seen
it would be difficult to swap the cables on one side without flexing the other side. (Unless the sensor is
securely mounted to the wall, etc.)
Thanks for the idea about the change fixing something with some flexing...
I recently spent some time on the bench at work with just such a problem - I was trying to take
measurements on a circuit board and they would jump back and forth between two values. I
wiggled everything and swapped out the coax cables, attenuator, etc. before putting a second board
in place and the problem went away. Apparently the first board had an intermittent contact in or
around the output connector.
A common cause of this in ham equipment is a PL-259 center pin with too much solder on it
that spreads the contacts on the SO-259 jack. Then contact can be intermittent when a plug
without the extra solder on the pin is inserted.