A lot of dust in the house is a symptom of high air infiltration rates. A infra-red imaging and blower door guided air sealing effort is going to be "worth it", but you may be able to locate an seal some of the large air leaks before taking it to that point. Contrary to many peoples' impression, sealing up the house will usually improve the overall indoor air quality, while reducing the dust accumulation. Only if you're lucky would you be able to seal it up tight enough that active ventilation would be an absolute requirement, but even leaky houses need at least some active ventilation, since the leaks don't always come via the cleanest paths, or supply the air or exhaust where it's needed the most.
The notion that ducted HVAC systems "clean" the air isn't always
well founded unless taking it to the HEPA extremes. The air only
circulates when there is a heating or cooling load, and those loads will
be smaller once you've dealt with the building envelope issues. You might consider a heat recovery ventilation system using much smaller ducts for improving indoor air quality issues. (Sometimes that's easy, sometimes not.) With heat recovery ventilation the incoming air is pre-heated by the exhaust air, which allows high ventilation rates when you want them without adding a huge heating & cooling load.
The
99% outside design temp in Dayton 45458 is +5F, so at a base temp of 65F that's 60 heating degrees. The past 12 months Dayton had 4691 HDD according to degreedays.net data sets. Assuming the same 102.36 million BTU from the previous WAG that becomes 22,673 BTU/HDD, or 945 BTU per degree hour, for an implied heat load of
~56,700 BTU/hr. Rectifiable air leakage could easily be over 10,000 BTU/hr, and taking that load off with air sealing is cheaper than the extra tonnage of heat pump required to support that load. Getting a 3000' rancher down to 15 BTU/hr per square foot of above-grade conditioned space @ 0F is usually pretty straightforward, which would put you in the 40,000 BTU/hr range @ +5F.
An open hearth fireplace is a major 24/365 infiltration driver. An air tight wood burning insert or if the firebox of the fireplace is cavernous, a wood stove with a big viewing window is probably going to be worthwhile investment if you burn much wood, since that will improve both indoor and outdoor air quality, and impede a known parasitic loss (the open flue). When installing the new wood burner take pains to air seal as best you can where the new flue liner enters the flue. The usually install a metal air barrier with a hole in it to accommodate the liner, but the quality of the air seal is all over the place, and often quite poor unless you impress upon the installer that it's important to you.
The open areas can almost certainly be heated & cooled by ductless air source heat pumps (mini-splits), but you'll need a room-by-room Manual-J to be able to size them correctly, and it's better to have a disinterested third party such as an engineer or RESNET rater run those numbers, not an HVAC contractor. With the Manual-J in hand you have enough information to vet the sanity of proposals as they come in.