Well, I landed here so got my answer. Probably the same issue as everyone else and no point moaning, I know only too well what it's like to be seen as an infinite resource. Instead, I'll share a workaround which may only be good for my particular situation.
This will be easier to understand by looking at the attached file and, vice versa, what I add here. No apologies for the unconstrained sketch etc, it's just to illustrate the point.
I have a shape (profile) with a series of almost but not quite parallel lines. (This is why offset planes won't work here). I need a plane at an angle to each of these and the plane angle needs to be identical. I want to then create a profile sketch on each of these angled planes. The profile is almost identical on each so I want to create it on the first angled plane, then copy and paste into sketches on each of the other angled planes; and then make some small tweaks to each sketch such that each of these profiles is unique. Ideally I want each paste to be in exactly the same place on their respective sketches, as each one is connected to a common edge.
Using plane at angle gives me two different outcomes, some planes are angled to one invisible reference, some to another, so not much use. I can play with the angles to get them close enough but it's a bit of a bodge. Un-suppress the first group in the timeline to see what I mean. But in any case, when I copy and paste from the first new sketch, it is placed randomly on the next sketch, and the next, etc. Of course it's not truly random, software can't do that, but there seems to be no way for me to predict and control for where it'll be pasted. On the attached example, they are mirroring. On the real project, they can be mirrored, 180 degrees rotated etc. Big PITA as the real profiles are a little complex and it takes ages to get them sorted out.
I next tried plane through two edges. supress all but sketch 1 and group 2 to see this. An improvement. I made a dummy copy of the 'lines' sketch and offset this, so I have two parallel edges for the new planes, thus ensuring they are true to each other. But when I copy and paste the profile sketch, I still get random mirroring. I guess this is something to do with what these angled planes pick as an invisible reference. Anyway, better but still no good.
What seems to work is plane through three points. Suppress all bar sketches 1 & 6 and group 3. Similar to the previous, using an offset copy sketch. Two of the points are off the top line, the third from the copy sketch. Identical methodology for each angled plane. Now, the copy and pasted sketches paste reliably and predictably. I'm guessing that the three points become a reference for the respective sketches.
I have no idea if there's a better, easier way but this looks like it'll get me through the issue that brought me here this evening.