The PIC numbering system was getting me confused so I spoke to an engineer at Microchip and this is what I was told...

The 12 in the 12F629 means it is an 8 pin chip. (I didn't ask why 12 means 8 or why they just didn't just call it an 8Fxxx)

The 6 after the F means that it has a 14 bit memory core, since anything other (? # > 5) has a 14 bit memory core.

A 12F5xx chip would be an 8 pin chip with a 12 bit memory core...

So it does not seem to a 12-bit core problem but rather an overall memory problem.

The 12F629 has 1k x 14 memory (there's that 14 bit core again), where as
the 12F1822 has 2K 14 memory.

I ordered some 12F1822s to see if I can get Darrel's program working.