Use the SS!
Switch to drilling on the lathe and keep the Shopsmith.
Alternately, use the horizontal boring function of the SS to cut down on the changeover.
The HF lathe and Drill press are sub-standard to the Shopsmith IMHO. Use the money you would spend on those and get good chucks and other tools.
Here is my sequence using the SS This will make sense to SS users, it may not make sense to standard lathe users, so take it as it comes. This is MY WAY of doing things, other people have their way of doing things, use what works best for you.
adjust speed to slow if you haven't already.
Mount either a scroll chuck or collett chuck to the arbor on the headstock. Use Scroll chuck for square blanks and collett chuck for round blanks. (I have PSI Barracuda 2 for scroll chuck and PSI collett chuck. Both use the 5/8 SS adapter from PSI)
Mount drill chuck in tail stock. Drill Blank by advancing quill slowly onto the drill bit.
Remove blank from chuck.
Swap chuck for sanding disc on headstock.
Glue tubes into blank.
Mount appropriate size rod/drill bit into drill chuck to hold tubed blank for squaring. Square the blank by just touching to the sanding disc. (I use cut off carriage bolts in different sizes for this. It also helps to adjust the eccentric off center towards you)
Switch drill chuck for live center or mandrel saver and check alignment with headstock/mandrel. (I have 2 eccentrics one has my live center, the other has my drill chuck mounted.)
if you are using a mandrel
Swap sanding disc for mandrel on headstock (I use the PSI shopsmith mandrel)
Mount blanks to mandrel turn and finish. (adjust speed as required
for efficient turning based on material and tools)
Remove blanks from mandrel
Remove mandrel from headstock
If you are turning between centers
Swap sanding disc for chuck with dead center.
mount blank between centers
Turn and finish
Remove blank
Remove chuck from headstock
Remove eccentric from tailstock and mount custom turned hardwood block into tailstock where the eccentric goes. (I just turned this between centers and it works really well. I also use it for dis-assembly if needed.)
Use the quill as a pen press by placing the components to be pressed between the arbor and the and the hardwood block.
Done.
Again, this is how I do it. I don't have room in my garage for anymore large tools, and I wouldn't trade my SS for anything (I'm also the third generation user of this 1955 SS that was handed down form Pa-Pa to Dad to me.)