When I have that issue of broad heads dropping, first thin I do is nock the arrow with cock feather IN rather than out... see if it then flies high, or spot on... which usually indicates a point, shaft, or nock alignment issue.
I have a cob job spin tester, and highly recommend you rig one up to spin check. Can be as simple as a couple pair of crossed nails on a piece of scrap lumber. Or, a couple bucks at the local hardware store for some roller bearings (lots of kinds available). This rig will also give you an excellent reading as to whether the shaft itself is straight.
Also... while "shooting the same weight BH and field point" is highly touted, you might try going up or down a little on BH weight and see what happens.