Finally bought a heat gun and completed this repair. On the broken line, it took 7 attempts to figure out a system and muster the confidence to proceed onto the new line.

For you future readers, the trick is laying the heat gun on a table while rotating the fitting in front of it. Every few seconds give it a pinch (leather gloves) and feel how pliable it's becoming. If you go too far, the line collapses while inserting the barb end.

Thanks to all who contributed

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1981 240D 4sp manual. Ivory White.