I just looked into SOLIDEDIT - Face - Color options and after you pick single face, you can type ALL to select them all - BYLAYER is then default choice when color dialog pops up...
What version of ACAD do you have - maybe this isn't functioning with your case... I tested this on A2018...
BTW. What happens when you just select 3DSOLID and switch it's color to new one and then restore it back? I suppose CAD should change all faces to object color you've chosen...