Control over Remove Overlapping Lines order

Is there any way to control the order ‘remove overlapping lines’ operates in? I have a number of interlocking shapes and I want to cut each shape out going from left to right with the ‘skipped’ line always being skipped in the second shape to be cut, never the first. Instead it seems to be random (I’m sure it isn’t but it looks like it) where sometimes the skipped line is in the first part, and sometimes in the second.

I’ve tried forcing the cut order by using groups and specifying ‘order by group’ but that makes no difference. That seems non-intuitive. I’d expect a complete shape in a group to be finished before starting another group, but that isn’t what happens with overlapping lines.

Order by Priority doesn’t work as I would expect either when using remove overlapping lines and lower priority lines are often cut before higher priority ones when they overlap.

What am I missing? It seems to me that ‘priority’ should always win, and higher priority shapes should cut first.Remove overlapping lines shouldn’t override that priority.

Thanks for any insight!

PS - I see that this problem has been reported before, but not answered. See here: Optimization: Order by vs Remove overlapping lines priority

No responses so far. What would help is an answer to the question. Is it expected behavior that ‘remove overlapping lines’ should ignore the cut order set by groups or priority?

If it is expected, then I can give up experimenting and stop trying to use that setting. Instead I’ll move parts so they are completely separated and not use the remove overlap option. That will work of course, it’s just a waste of material and time.

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