I can’t help you with advice, as I’ve never grown borage. However, I have seeds and am about to start them, so thanks for posting this. Knowing that I should expect seeds to “self eject like stuntmen on steroids” is very helpful.

I’ve done it before. I found that if I broke the taproot, I usually lost the plant. Get them when they are small, so the taproot isn’t too big, and give them a good break in part shade after transplanting. I usually put three or four plants in each pot, figuring on losing a few. Every once in a while I had a pot with extras, but usually only one made it.

I have borage in my garden too. Same story for me, lots of seedlings.
I also tried to transplant in pots and found it was not always successful for the reasons mentioned above. I decided that if I wanted to give a go at selling some seedlings next year, I’ll just get the seeds and plant them in long milk cartons so they don’t get disturbed. The seeds have high success rate.
I find Borage an exceptionally good plant. Lots of uses, my bees love them and my ducks and chicken too. it goes a long way as I do use the leaves a lot but they do reproduce just as much ;)
It looks good in the garden when it’s full of blue flowers too. I crystalize the flowers for cake decoration or put them in ice cube trays to look good in summer drinks, the young leaves are great chopped in salads or in soups.
It’s all good! :)