Yes as Midlife says, for most of us it's a hammer and drift job, but try to keep the cup parallel with the tube, as it (hopefully) emerges..
There seem to have been a few different Levins over the years, with different stack-heights. The one you linked to could be 80s? Same style as Stronglight A9 I guess- sort of streamlined. The Levin I was thinking of is actually a dead ringer for Campag. Super Record Strada but with slightly less stack.
I confess Finney I am no longer sure what
you are measuring
but at the risk of stating the obvious- You have a steerer tube of a certain measurable length, and a headtube of a certain measurable length, regardless of any headset bits attempting to thwart your measuring. The difference in length between them is your stack-height. If some of that difference is not at one end of your head-tube, you can bet your life you will find it at the other end!
Also - was it usual to put a piece of tin can inside the compression rings in a headset BITD?
Don't worry unless it was/is being used as a shim to restore 'interference fit' between bottom cup/headtube and/or top race/headtube. If it was/is, then something is badly worn, hopefully the headset, and not the head-tube.