You're not going to believe this.
I placed the blank PIC into the programmer, did a blank check (checked "OK!"), performed a 'read', selected the HEX file you provided, selected Intel, the blank check box was already checked, and programmed.
It programmed in 01:70.
For laughs I did a blank check and it showed: chip address 00000000, chip data 2855, buffer address 00000000, buffer data 2855, and showed 'error' for the blank check (as I assumed since it's now programmed).
I also 'verified' and that check "OK"!.
Soldered it onto the board, turned on power, the green LED came on, the soldering iron heated, and the green LED never turned off. I touched solder to the tip and it melted indicating it's at least 360 degrees F, turned the knob to minimum, and the green LED remained solid green. Increased the knob, let it heat more, turned knob to minimum, and the LED remained solid green.
Thankfully before turning off the programmer I saved the buffer and info that was read back from the newly programmed PIC (see attached) should you decide to look at it.