Another update:
Using the internal 4 MHz clock, I wasn't able to communicate at rates higher than 19200 baud, because the error gets too high. It appears that a 3% error is OK, but above 19200, the error is in the 7% range and communications fail. I remember having read some asynch protocol standards many years ago that specified how far off the baud rate could be and still get good communications, but I don't remember what the numbers would be, though 5% rings a bell.
Anyway, the FTDI driver on the computer can be set to non standard baud rates. So, I picked ones that the PIC could generate exactly. After that, the communications have been flawless. I now have communications working perfectly at 250k baud which is faster than the PIC can generate data to send. Needless to say, I'm very impressed.