Fletcher, with arrows at the lower (AMO measured) FOC’s I think you might be able to notice a flight difference changing from a field point to a long broadhead and measure a significant difference in the balance point along the shaft. That’s because, at the lower ‘AMO measured’ FOC’s you’re getting a ‘meaningfully’ longer forward leaver arm by moving some of the weight a bit farther forward. Because this will change the relationship between the Gravitational Center (GC) and the Center of Pressure (CP) of the arrow in flight it is going to cause a change in the TRUE FOC. It has nothing to do with the overall length of the arrow, merely the change in the relationship between the GC and the CP.
At the higher amounts of (AMO measured) FOC’s changing from a field point to even a very long broadhead makes less than a 1mm change in the location of the balance point (extremely hard to measure accurately). That’s because the forward lever arm is already extremely short and it takes a lot of weight change to make a significant difference. Using a hooter shooter, at those higher FOC’s there is no flight difference between field points and broadhead. (I know that you already understand all this, but the explanation is for those that don’t know.)
In a nutshell, the higher the arrow’s (AMO) measured FOC the less difference there will be between the GC and CP as one changes between a field point and a BH.
All that notwithstanding, since it does not reflect the true FOC I still see our relative FOC as merely a reference point for duplicating arrow setups. As you noted, without some pretty sophisticated measuring equipment we’ll never be able to accurately state the true FOC. As long as one states the measuring methiod used to determin the realtive FOC it really makes no difference which method we use. Since the true FOC depends on the relationship between and GC and the CP, and the fletching we use CAN have a large effect on the location of the CP it’s likely that we SHOULD be stating the fletching used in every setup too.