Welcome in the forum, Gord.
The processor of the Cy8C27xx and the Cy8C29xx are quite the same, only the 27443 has got 16K flash and only 256 bytes of sram. Hence there cannot be a large code difference.
The PSoC Designer is a bit outdated, I would suggest you to update to current version which is 5.4
Check if you set the Firstblock to 510.
Check if you modified the flash security to allow writes to the required blocks
Firstblock is set to 510 and the flash security is set to U for the last 2 blocks but I cannot get it to write.
Would you have a assembly code snippet to share?
Only code snippets are in datasheet for eeprom. Check your stack and stack setting.
Switch over to PSoC4, more modern, cheaper, debug capabilities, but no DIL-package. Check the prototyping kit CY8CKIT-043.