Even if you price CO2 emissions in, both electricity and natgas rise - because of how much electricity is generated by gas - and how inefficient thermal generation is.
1 metric ton of carbon is about 19 Mcf of gas burned.
19 Mcf of gas contains about 1.65MW of electric power (assuming combined efficiency of generation and transmission of 30% - if you can provide a framework for better electricity efficiency I'm open to it).
It'd add about $121 to the price per MW or 35 cents per 10,000 BTU
It'd add about $10 to the price per Mcf of gas or about 10 cents per 10,000 BTU
Assuming that 50% of your power has a carbon surcharge on it, we can halve those numbers - 17.5 cents per 10,000 BTU.
So once I plug those into my HP Calculator - that raises assumed electricity prices to 90 cents per 10,000 BTU and gas prices to 24 cents per 10,000 BTU.
The heat pump still ends up being more expensive over the entire operating range - note that HP efficiency goes down with temperature.
So at 40f it costs 35 cents on my 5T HP to generate 10,000 BTU of heat, at 10f 65 cents per 10,000 BTU of heat. Gas however is steady at 29 cents per 10,000 BTU of heat - no matter the operating temp.