The Cummins is a 1990 engine with a 1991.5-1993 head.
When I took the 7mm injectors out, I found no copper washer to set the spray position in relation to the piston.
Would this be normal when using a later head with 7mm instead of the 9mm injectors?

 

There is supposed to be a washer. It may be stuck in the bottom of the hole. As far as washer thickness, all aftermarket injectors use the thinnest washer because they are slightly shorter than the stock ones.