One trick when opening the brake lines, for example to install ss brake lines or to rebuild a caliper, put a jackstand or something in the car and set it so that it pushes the brake pedal, this seems to close off the line at the top (similar to holding your finger on the end of a straw) and it minimizes the amount of fluid that leaks out.
I would replace the SS lines, and then do your flush, as adding the SS lines will introduce a lot of air into the system and will require a major bleed after.
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