Search under BLUE BEACON, a chain of truck washes as several owners use them. My experience is in using them to run a Peterbilt through. I'd take some time with the manager at an individual location. One might also start by contacting the company directly to ask for assistance.
The method used to wash is known among power washing pro's as two-stepping where the preservation of time & energy is paramount. One wishes to avoid having to brush a vehicle to get it clean as it is terribly time-consuming due to inconsistencies in results (the small corners that get missed). The business of washing fleets of trucks is to the near-lowest bidder. And the cost per vehicle to the bidder is the main incentive to get things right. Now, two-stepping is using an alkaline and an acid cleaner in succession to get the vehicle clean without brushing. Leaving out the difficulties of local conditions the method is successful.
BLUE BEACON uses an alkaline followed by an acid wash. Pressure, soft water, good tools, and good training of personnel alllow them to offer consistent results. As fleet accounts are the bread & butter of the business I believe you will find the location manager interested in solving your problem. He or she actually does have some leeway in how things are done.
IMO, as leaving pollutants mixed with dirt, road grime, etc on a vehicle surface is worse than worrying over "perfection" -- and that this method is better than the usual I'm-on-the-road-and-using-coin-pressure-washes to get the bug grime, etc off -- I'd make contact nationally and locally.
Yes, look over the TT and see where one should direct the managers attention to in turn direct his employees. Maybe make up some covers for intake/exhaust ports, etc.
I don't mean for this to be an ad for BLUE BEACON as they are not as good as some locally-owned washes. It is a tough business with environmental water handling issues. But my experience has been good, overall, per trucks. As my TT's have jalousie windows, some shrunken window seals and maybe not-perfect door/compartment seals, I'd have to do a look/see around this.
But getting the dirt off of the front and lower beltline (vehicles get dirty from the ground up, not from top down) means much of the "upper trailer" does not need as much work.
A good wax job on the TT makes it easy for everyone to get stick bug & bird goo off. It's not unusual for me to have to clean windshield, side glass and mirrors three times daily on the Pete. To that end I use RAIN-X on the glass after a solvent is used. This makes the cleaning much easier (as the windshield is, what, eight feet from ground level?)
BB does not wash the roof, per se. The occasional BB type cleaning to keep the worst at bay until the owner does his usual roof-down cleaning may be the best use of this type of business for a TT owner while on the road.