Their "system" is a computer system, right? Even if the teachers don't think they can change something mid-year, I would bet that there is an IT administrator that can do whatever they would like. They just haven't had to do it before.
FWIW in 3rd grade my DD11 took 4th grade math and they had her take the 3rd grade math testing. Same in 4th when she took the 5th grade math. This was a major pain because they felt the need to pull her from her actual class to "review" the lower material. Finally in 5th grade, the district just gave her the 6th grade test. I know it's not exactly the same but give it some thought as to what you think would be ideal wrt the testing.
Also the district did finally figure out how to list the correct math teacher in the computer system vs the lower level math teacher having to enter the grades.
Good Luck
