Using an FPGA does not imply high cost. Its flexibility may save a lot of trouble, like board revisions. Appearently the OP has a problem there, too. And as you wrote, it won't be a $5 MCU anyway, due to record size.
It seems to be difficult to do it on a MCU, i mean selecting a MCU with the proper peripheral. If i hear that somebody found a trick using two instances of an SAI peripheral, that's also nothing to recommend.
Implementing a peripheral by bit-banging isn't always possible. That's why we have this thread.
Regards, Dieter