Eagle1.......
It appears that you do indeed have a pretty consistent charge drop of 4+gr, judging by the agreement between your three scales: electric and the two beam scales.
From the Hodgdon loading tables, it appears that you want to load 147gr Hornady XTPs @ 800fps, which is a 3.0gr powder charge. Nice, conservative, low velocity target load. Here's hoping that you don't have any 4+gr charges loaded, because that load is off the chart for those heavy bullets. Might have to use your bullet puller, if so. Or dump whatever is already loaded.
You probably know all this already: If you're using the micrometer on the Lee Perfect Powder measure as the primary indicator of the charge weight, it just doesn't work that way. The LPP measure drops the powder charge by volume, not weight. No matter what the charge micrometer gauge on the charging handle reads. When setting up, you gotta drop a test charge first, then weigh and adjust the micrometer until the charge weight drops just right. Basic reloading procedure. Which you most likely know.
If you drop a long string of charges before rechecking the charge weight, some powders actually "pack" in the powder charge chamber and become more dense. It's the pepper shaker effect. If you fill a pepper shaker full to the top, put the lid on, and tap it on the table top, shortly the pepper will pack down and a space appears at the top of the shaker. The pepper is now denser and a given volume weighs more than previously. Same w/some powders. Happens because of the tapping effect from the charge handle.
So--you might be experiencing that kind of phenomenon. Or, if the micrometer isn't locked, constant tapping may open the charge chamber to larger volume.
You said it best: Weigh the powder charge. Every few charges, at minimum. [Beam scales properly zeroed out seem to be the most honest.]
And---doesn't sound to me like you have too much reloading stuff. Not yet.