Without a literal dollar figure, it is hard to say.
There is a premium on travel, and field work. A lot is going to depend on your office culture. I know quite a few firms where field engineers have a rough job and the guys back at the shop work 9-5.
In a larger company, your role change, likely comes with a title change in the "HR" department (from something like "SALES ENGINEER" or "FEILD ENGINEER" to "ENGINEER I/II/III). Every one with the same shadow title is probably stuck in some "pay band". By keeping these bands tight you avoid a lot of potential for discrimination lawsuits. You might not see the pay cut at a smaller company but the title change at a bigger company makes it "likely".
If I look at your 1 and 2 options, ( 1. Take their offer and move on. 2. Take a stand with a potential of being forced to resign. ) There really isn't a difference except your pay while looking for a new job. "Forced to resign" is a misnomer, and I know people who have spent years on PIP's as employers tried to squeeze them out doing little and collecting a check. There is also the "your fired" speech, it is an at will state and you never know if your HR department has a wild hair up their ass.
I suspect that no matter what you choose to do, it is time for you to start looking for a new job.