The significance of the accent is not the fact that it's old, it's the lower class impression that it gives. Translating it as, I dunno, Shakespearean Early Modern English or like she's Jesus in the KJV Bible just because it's "old" would be the completely wrong thing to do because the effect would be almost the polar opposite of what's intended.
When you translate language A to language B, the entire intention is to remove the A part and replace it with B. There is no language pair where the connotations are going to map one-to-one because the cultural circumstances around each language are, obviously, always going to be very different. You cannot avoid "removing the old Japanese part". You can't magically inject "old Japanese" into English. You do the best with what you've given, and that's to use English that makes the English reader feel like the Japanese reader does, as best as you can.
Matsuri being half-English was a happy coincidence as far the dialect decision was made, not the primary motivator. Even though I understand the point about the grandparents not being British, it's a surface level complaint to us. Even if she had nothing to do with England, we most likely would have picked the route we went anyway, because the connotations match decently enough that there's precedent in "real" literature making the exact same choice we did in both directions, Japanese-to-English and vice versa.