[old ugly]

i would guess that stud is 7/16nf that is the only size i have seen.

other than changing the rod the only cheat i can think of is. find the metric size die that is a wee bit smaller that will cut nice threads onto those studs. i don't know what is just a bit smaller than 7/16 but there has to be one. cost nothing to try.
if you do that you will need to find castleated nuts or at least some way to lock it.
i would not worry about balance.