Charis, if you use your lathe as sort of a boring mill, then the steady would be unnecessary.
Fabricate a cradle to secure the tube centered, attached to your carriage and a second support that is placed near the right end of the lathe bed, that has some mass and is confined to slide on the ways, like a loosened tail stock.
The cradle could be as simple as a 1/2" or greater thickness, V'ed plate, drilled to bolt against your carriage, like most follow rests do, a locating shelf milled across, to solidly seat on the carriage, the top corners of the cradle drilled and tapped vertically, to tighten down a cross bar, use padded vise chain....or...
A cable or tie-rod, between the carriage and tail stock, the part secured in the carriage cradle and a pipe center in the tail stock advanced into the part, tensioning the cable/rod 'til the assemblage is ridgid. A little extra way oil....
Then a boring head mounted on a shank that matches your lathes spindle taper, (#5MT on my 17") or a straight shank that you can mount in a chuck, carriage feed doing the work.
I think that I'd arrange the seats of the cradle(s), as non-marring, smooth-topped brass bolts, say 1/2", radiating inward @ 120° and 240°, (top being 0°), with lock nuts, making centering on the lathe easy and making the fixture adjustable for other diameters.
A fixed stop, say a downward projection of the cradle that stops against the front or back way, could be incorporated to quickly center then lock the cross feed each time the fixture is mounted.
I have several shop-built fixtures for my 17" lathe that require removing the compound, no problem, just 2 bolts. That should easily provide for a 6" + swing over the carriage.
My shop is not nearly big enough for all the machines it would take to equal the versatility of my fixtured lathes and mills, while my investment is a tiny fraction. To me, the way to go for seldom but repeated jobs.
A V-block fixture secured to the table and the boring head in my K&T horizontal would quickly set up the job for me.
Bob
Edit: see what happens when you type too long......