Tell me more about how you arrived at 0.003". I'm 100% confident Dabbler knows his stuff but will throw out some food for thought just in case.
If you put the test bar between HS & TS dead centers & then measured the MT taper, that presumes that the TS axis is 100% aligned to the HS axis. But if your TS was say 0.002" in/out or up/down it would yield a false MT reading. Picture this scenario if it was a parallel bar like the Edge tool, a DTI measurement difference has nothing to do with taper, its TS position related. But if you first ran the DTI down the straight section of the test bar & that was 100% parallel, it gives confidence to TS position & is the right step-1
When you measured the taper, I assume you held a DTI in toolpost, ball exactly on bar center, contact a point on thick end, zero DTI, move carriage over 3.000", contact ball on thin end to DTI zero, obtain cross feed delta & compare that against MT taper spec... something like that? I think I get 0.0753" on a 3.0 X displacement. But its highly dependant on the inputs like same backlash direction & dial accuracy. Do you have DRO on these 2 axis or reading off the dials? The other big thing on tapers is if the ball is not precisely on center, then as you jog over, the ball will ride up or down the taper & exaggerate skew the reading big time. This could happen if for example your TS was high. Lots of them are apparently high 'to allow for wear' which I've never understood.
Anyway, if you guys checked this stuff off, that's the extent of my experience & I guess maybe you have a dud bar in terms of taper angle.