We have addressed this topic of common assessments in hundreds of ways over many years here. My thinking has evolved to keeping them separate from your CI instruction. Mixing the two doesn’t work. This is the opposite of the TPRS model.
My recommendation is to take the first half of class to teach and test the common assessment material in the traditional way and make sure the kids pass the common assessments with no problem. This gets your traditional colleagues off your back.
Of course, if you are all a totally CI department you are blessed – you don’t have to concern yourself with boring ways of teaching from the past that are proven not to work.