Filing jointly doesn't matter where the money comes from.
I fairly often make a first quarter estimated tax payment (and only that one for the year) to cover stuff like this as its just easiest (The first q payment is due at the same time I'm doing all my other tax stuff, etc, and if done first quarter of course its not late, etc, and I consider the 'loss' of paying early whatever the Money market interest on the money is, so here we're not talking about much...).
Of course, it sure seems unnecessary to do this here for multiple possible reasons, including given you worked half of last year and your conversions will be about the same that you're gonna owe less this year in total, and thus are covered by the safe harbor and can just wait and pay it all next April.