You can make the checks needed with an indicator.
First, the indicator will be mounted on a bar at least 8" long and rotated while mounted to your lathe spindle.
It can be clamped in a chuck or collett.
Soo, you'll need to make certain that the bar and indicator won't sag or have other errors.
Simply chuck the bar with indicator close to the lathe spindle, indicate to the inside of the tailstock spindle with
all locks snug on the tailstock. Record the readings.
Move the bar out 6" and set the tailstock back the same, read again. Since any bed twist will be too small to register in such a test, unless it's a pretzel,
you will see any misalignment of the head.
Don't worry about reading on different areas of the morse taper. Your only looking to see the difference in the sweep readings.
This will show lateral and vertical alignment problems.
I must agree with others that the footing needs to be better.
Just a piece of 3/4" plywood to spread the load out with some 4"x 4" x 1/4" thick plates will make a large
improvement in the setup.