Thanks, Mensur. I'll see how well it goes re-aligning. My issue was that it may need to be done repeatedly for work (maybe 100 times?). Or some large multiple of a few hours.
And I also see caveats for the few faster solutions I've found in the past few hours, like mafft --add (https://mafft.cbrc.jp/alignment/server/add_sequences.html).
So maybe I'll try out the faster solutions and compare with the re-aligning results, and then if they look very different give preference to the re-align? I don't want to find out later that all my results are flawed.