10 air changes per hour is a lot; I believe the current recommendations for average climates is 3.
And we're looking at the margins; 1 air change per hour can do wonders for preventing the spread of disease and improving air quality, compared to 0 air changes per hour.
Nevertheless, I redid your math, and found that your hypothetical home has 26,728 more BTUs of energy in its air, compared to the outside air[-1][0][1], and that the recommended furnace for such a climate should be 160,000 BTU/hr [2].
Using those numbers as a base, I find that, with an efficiency of 95%, it would require 120 (that's one hundred and twenty) air changes per hour to double heating costs.
With 60% efficiency, it would require 15 air changes per hour to double heating costs.
And it only takes a few air changes per hour to increase comfort and prevent illness.
[-1] I suddenly realized that the google search links that I used for these calculations are messy and unwieldy, so I'll summarize my calculations: (2600 ft^2) * (8 ft) represent the volume of the house; (1.225 kg / m^3) represents the density of air, (1.005 kJ/(kg * Kelvin)) represents the specific heat of air, (70 * (5/9)) represents the temperature difference you gave me, in Kelvin. Multiplying everything together, and letting Google automatically take care of unit conversions, gives me 28.2 MegaJoules of energy in the house.
[0] https://www.google.com/search?q=%282600+ft%5E2%29*%288+ft%29...
[1] https://www.google.com/search?q=convert+28199142.9+joules+to...
[2] https://www.pickhvac.com/calculator/heating-btu/