With a 36" long 1.125" diameter rifle barrel blank, I have the barrel
mostly slid up into the headstock, dialed in on the bore in the 4 jaw,
and cut the outside to be round.
I take the barrel out, turn it around, dial in, and cut round the other
end of the barrel.
I slide the steady rest up next to the headstock and locate the three
roller bearing of my steady rest on the round part of the barrel.
I open the top of the steady rest, move it to the right end of the ways,
loosen the 4 jaw, slide the barrel out of the chuck partially to reach
the steady rest, dial in the chuck on the round part of the left end of
the barrel, and then clamp the steady rest on the round part of the
left end of the barrel.

When I made the bottom part of my steady rest, I was careful to build
everything very stiff. I can go from loose to fully tightened with 1/8
turn of the steady rest lock down.
If the steady rest can change height with how much it is tightened, that
is no good.

--
Be careful what you pray for, it can happen.