I have a friend who owns a house in Montana. His fridge is on an AFCI breaker that trips every time they have a power failure. In Canada, we don't AFCI fridge plugs. Do you not have an exception for fridges?
Are you allowed to install an AFCI in a box beside the panel. I wonder if it's the make of the breaker that is the problem.
There are rules about how to do it but generally yes you can use a device type AFCI in the first outlet on a branch circuit if it is less than 50' away (wire length). The easiest way to comply is to use a piece of MC cable between the box and the panel. If it is a straight shot you could even use a piece of EMT or a close nipple for a side by side install. It just has to be in metal.
Before I did all of that I would try it on a GFCI only circuit. If that trips look inward toward the fridge. It is not uncommon for old fridges with bad compressors to trip GFCIs.