Framing error if I disable transmitter after shift register is empty?

[richard]

there is another issue with that chip

from data sheet async reception chapter

Should I set LatC.6 to 1 when I disable the transmitter?

no , it will look like it works but the pin is now hard driven high , not tristated at all

I thought the pull-ups were supposed to handle that?

if the pin was tristated then it would

And I don't know how to "make the tx pin open drain"; I've never done that

.
that chip cannot do it, more suitable to task chips have a ODCONx register

I don't honestly don't understand why you consider it not a decent chip?

poorly suited to task at hand in my view