Cherie, I find that that cotton picking nib is hard to get a good reading on with calipers. I try to read it parallel with the jaws such that the nib just passes through the jaws by just touching both at the same time.
Try holding the nib by the nose cone with your thumb and fore finger and measure from the press fitting side. This is the measurement you want as this is where the nib meets the barrel. Use the same holding technique for the finial as well.
The tapered end of the blank can be even worse. There you must be using the sharpened tips of the calipers. If the blank is turning, then you will cut a real nice ring into the blank, or so I have been told,
Don't measure with vernier style (digital or analog) calipers while the lathe is turning.
You can damage your blank by scratching it, those sharp points are sharp enough to scratch.
The jaws can catch and you will need a new set of calipers.
This is a delicate instrument and excessive wear from rapidly spinning objects will negatively affect your measurement and possibly cause wear on the machined surfaces of your caliper.
Do measure from different angles. Take a measurement and take note, rotate the blank by hand 1/3 or so revolutions and measure again, repeat process, this is a good way to check if you are going out of round.
I also recommend switching to finishing bushings at the point where you start to measure with calipers. This not only adds the clearance needed for finishing but also provides more clearance for the calipers as well.
Just my thoughts on measuring. I have stopped purchasing bushings and make my own finishing bushings. There are lots of posts and articles on this.
Terry