I wouldn't be happy with 10 minutes either -- 60 sounds better and you can always use your nose to guide you.
My house is roughly 2700 sq ft. How long do you think it will take the air to be replaced a sufficient number of times
2700 sq ft with 8 ft ceilings is 21,600 cu ft, so the rate at which that can be changed would be based on the CFM of your fans.
If you have an externally vented range hood for example, those are usually sized at 400 cfm for an electric range, so 21,600 cu ft / 400 cfm = 54 minutes (I'd probably double that because they aren't perfectly efficient). If you have externally vented bathroom fans, those can also be run and their CFM rating would further increase the air changes per hour.
The benefit of running your HVAC fan during the air-out is that it will help in the mixing of fresh and stale air which might otherwise get trapped in rooms without much air flow.
If I use box fans, too, do I point them in or out?
If you have a pair, point one blowing out and the other blowing in and place them in windows that are on opposite sides of the house (as a bonus, observe the outdoor wind direction and work with that rather than against it). Since those fans aren't sealed in the window openings, they won't be as efficient as they could (still fine though), but that will help bring in fresh air at the same rate stale air is exhausted. In terms of a CFM calculation for these units, you'd only use the rated CFM for a single unit rather than doubling the rate with 2.
During the air-out process, I would leave a few times for a long enough period to overcome
smell adaptation -- your nose will be far more sensitive to any residual smells in the home upon your return.
