Bob,
Your process for drilling on the lathe will continue to give you this kind of "sloppy" holes. Lathes are able , with careful processes of giving precise results, or without those processes, sloppy results. See Don Ward's book or Doc Greens book on work holding as good process references.
I suspect your process gave you a lot more "slop" on one end of the blank (tailstock end). Unless you can even up the hole, you will likely not be able to "sleeve" the hole. A PSI 8 mm PENCIL tube makes an excellent slip fit sleeve for a 7 mm tube. You may be able to sleeve part of the blank and achieve a more concentric fit. A bit of epoxy or loctite will hold the 7mm tube in the sleeve.
You can also fill and redrill to provide a better concentric fit.
If being concentric is not a concern, just use epoxy and move ahead.