Thanks very much all for the comments and info.
So this morning I spent half an hour on the EN1A, and it immediately gave a much better result. Started wth the (un-modified) HSS tool:

Which gave a far better finish on this material. However, the second pass was nowhere near as good, with some ridges apparent.
So, gave up with that (again), and went to the GT insert, which gave fairly similar results, and more consistent in subsequent passes too:

After wrapping some abrasive paper and Autosol around it for a minute or so, I ended up with this:

Not perfect, but far closer to what I wanted. So GT insert, lubricated with oil aerosol and finished with fine abrasive and polish is what I'll do.
Also – Ramon & Jason's comments on getting lengths consistent: I've got a second-hand set of unashamedly uncalibrated slip gauges. I assume the procedure is something like this?
1) Put the tool against the end face of the workpiece.
2) Make a stack of gauges to the machined shaft length required:

3) Put the slip gauge stack between the saddle and the stop, and lock off (I made an adjustable stop when building the 10V):

4) Cut using feed up to about 1/2mm from the stop, then manually cut to the stop.
It seemed to work OK, although I'll need to lengthen the stop rod for this.
Quick question on procedure:
It was mentioned before to swap the rod after machining one end, so always machine at the tailstock. I suppose to get the diameters of each step precisely the same, I could rotate the shaft after every roughing cut, and final cut, such that the diameter setting would be identical for both ends? The only issue would be the length stop would rely on the centre drillings to be of identical depth, otherwise the lengths would be slightly off.
So is it best to complete one end, then swap and start again on the other, or do them 'simultaneously'?
To answer a few questions:
I'm using a grinding wheel that's a bit too coarse and a bit worn, plus a belt sander. During the conversations on grinding the boring tools ealrier in the thread, someone said that the stuff I was using was better than theirs and shouldn't be an issue, so based on that I've just cracked on with it. The boring tools I ground worked fine eventually.
Re. flood cooling to get rid of the chips – I did think that might be an issue, so experimented with an oil spray can with the tube next to the cut, to flush the chips away – made no difference to tearing on the 080A15 material, although for the final passes on the EN1A I will do it anyway.
The material 080A15 material I'm sure my supplier said it would be OK to machine, but then again he doesn't know the specifics of my equipment (or experience), so fair enough.
Ramon – I'm using brass bearing material, not CI or bronze. I don't think anyone mentioned that was an issue when I mentioned it previously?
Ramon – what is that part you posted – it looks impressive, like the clutch from the space shuttle or something?
Hopper – Re. feed rate: I can't remember the figure, but it's the lowest with standards gears, plus I fitted the one-piece fine feed tumbler gear you mention from Myford a long time ago. So it's fine-fine. Works very well on most other materials.
Thanks all.