Thanks for the additional responses Judy & grandmabee. I'm still pondering how to handle this, given the amount involved.
It's now clearly a matter of switching names IF we request that the overpayment be applied to 2018. But if I switch names and they STILL don't apply the $6,000 correctly, the client is going to be asking me every other day if I've corrected it yet. (Good client, but I know how they react when things don't go according to plan.)
On the other hand, if we file as usual and claim a refund, it's just a matter of IRS processing the return normally, sending a refund, the client cashing the check, and then making the Jan 15, 2020 payment on time. This more-or-less takes it out of my hands and puts the responsibility back on the client (and IRS). If there's a delay, It isn't due to anything I did or did not do.