I get a lot of that cylinder rod pretty easily. The 1045 ish stuff. Ocassionally a "good" one that's made of something real nice, but usually it's the "lego" cylinders that are made out of whatever they can get a train car load of for cheap, can induction harden, and get out the door quickly. You may well find that (within that family), while they're all similar, some rods may not machine just the same as others.
I do this on a South Bend 9A, so my horsepower and rigidity is well shy of where you are at, so take my observations for what they are.
I equate this stuff as being similar to working with stainless. You've got to stay under the cut in both directions. That is, depth of cut and feed rate. This stuff will almost always work harden on you. Not as bad as stainless, but it's headed in that direction. I have to take a smaller depth of cut than I like to, in order to increase the feed rate.
I find that carbide inserts take WAY more horsepower to run than high speed steel does. While this is always true, this material kind of makes it "more true". I get a bunch more material off with a high speed steel cutter. It does have to be a better grade, but nothing miraculous. After you get the chrome and the induction hardened layer peeled of course. HSS won't touch that. Not for more than a few seconds anyhow.
I find that the general cutting and some rudimentary and plausible, even if not great chip breaking goes easier if I can dial the speed back to just below blue chips. I like to see them come off "normal", and develop to "tan". That's when I'm sometimes able to get them to "flick" themselves loose at an inch or two, before they wrap up on the tool. No, that's not ideal. Ideally you'd be able to increase the feed until they break off in C shapes, or 9 shapes, but that's a LOT of horsepower. I'm not there by any stretch. I'm not sure if your lathe is in that range where it would do that.
That speed that seems to work best, it's usually below the recommended speeds. For carbide or for HSS, it's a lot easier to work with, and better finishes when I slow down some.
While bumping the power feed does break "unbreakable" chips, I've also found that (WITH ALL CAUTION AND RESPECT), if I've got a good strong coil going, I can use a long wire to guide it over the back of the carriage, into a plastic trash can..... That works quite nice IF that keeps it well away from any pertenant control handles. I'd bet I've got some in the bucket that are twenty or thirty feet long if I could untangle them. Again, use judgement and caution. That needs to be away from the controls, so if it should hitch up on something, you can get the feed stopped right quick and in a hurry, and without without being in harms way. I would also NOT do this if there was any chance that the continuous chip was anywhere near stout enough to pull anything back out of said trash can.
Again, this is not your lathe, but maybe you can get some tidbit out of that that you could apply to yours. The material is what it is, but once you figure out how to (reasonably) work with it... It makes good parts. If you can get your hands on it reasonably, it's worth the trouble.