it does seem like the antenna is just too long and that if you were able to get down to say 26.515, you might find you have a flat match.
I know that there is always a reluctance to cut a whip because you can end up with a whip that's too short, so my suggestion is to use a "fake" whip to get the length right and then cut your real whip to that length.
you can use anything from a straightened coat hanger to a length of solid copper wire.
it does look like a nice installation, but i suspect the reason you're noticing the change with the trailer hooked up is because of your chosen mounting location.
mobile antennas really want to have a big flat horizontal piece of metal right underneath them as a counterpoise.
any deviation from this is going to mess with the radiation angle and it may prove difficult to tune out any reactance. Just having a big chunk of metal under the antenna isn't really going to help unless that metal is flat and continuous around the base of the antenna.
I know this is not an option for you, but i would bet money that if you moved the antenna to the center of the cab roof these issues would go away.
one test you can do to see if you have common mode currents riding on the shield of the coax (which will mess with your SWR) is to move the coax around while watching your SWR meter.
if moving the coax around causes the SWR reading to change, then you have common mode currents and are going to need to put some ferrite at the feedpoint of the antenna.
hope this is at least somewhat helpful,
LC