Hi, Jim. Sounds like you've got it figured out, and I'm glad the tip to only extend a bit at a time helped, but I think the slow RPM and parting tool aren't making your life any easier.
I'm definitely still a noob as well, but I recently started taking speeds and feeds a lot more seriously with much better results because of it. Basically slower speeds are for heavier roughing cuts, and faster speeds for shallower finishing cuts, but you still want to be in the ballpark for your material. At 500 RPM you're only getting around 24.5 SFPM (about 1/3 to 1/4 as fast as you should be turning). Since you only need to take 0.025" off the diameter, you're basically just making a finishing cut. The references I use (laugh) say around 60-80 SFPM for roughing cuts and around 100 SFPM for finishing cuts on plain carbon mild steel (as they say, that's the great thing about standard references — there are so many to choose from!).
A center would, of course, help prevent deflection, but on such a small part it seems unnecessary. On really long thin rods you need a follower rest anyway — a steady rest still lets the part bend in the middle) — or continue to use the "step and extend" trick you're using now. The "three times diameter" rule of thumb says no more than 9/16" should extend from the chuck, but I'm pretty sure you could get away with even a full inch extended as long as you take off the full amount in one pass with a sharp turning tool (per my earlier comment: more axial load that way and less radial load).
I bet with a freshly ground turning tool, 3 or 4 times faster RPMs and taking the full 0.025" off the diameter you'll get much, much better results. I'd feed by hand, but if power feeding on my Logan I'd use the slowest or next slowest feed (0.004" or 0.008").
By
far the best article I've ever read on sharpening HSS tool bits is
Conrad Hoffman's treatise on the matter. Really great article, well worth reading and re-reading several times — some great info there.
Lastly, can you adjust your 3-jaw chuck for runout (sta-tru back or whatever the trade name is)? Otherwise, unless you're really lucky, you've almost certainly got enough runout to make it hard to turn small diameters and take the same amount off all around. Small, precise stuff is usually best handled with collets, the 4-jaw (independent) chuck, or old-school turning between centers. I only use my 3-jaw for rough and ready larger turning jobs. Buying some 3C collets and a closer for my old Logan was one of the best things I ever did — utterly changed my opinion on just how "loose and worn out" my lathe was.
Enjoy!
--
Rex