If there is a problem of warm stratified air against the ceiling then it would be accompanied by cooler unwanted stratified air against the floor. If a fan was set so slow as to not move air in the occupied areas then the other half of the problem, cooler stratified floor air, would not be mitigated. Not that I want to go there, but the best draftless way to deal with it is with low mounted returns.
One factor overlooked here...tolerance levels for air movement before one declares their environment to be "drafty". If air is set in motion by a reversed ceiling fan near the ceiling, it will affect the air movement in the entire room. The fan is forcing the overheated air to fall, which will displace the cooler air near the floor at the same time the warmer air is mixing with the cooler air, causing it to warm up and rise. Repeat cycle ad nauseum.
The velocity in the lower regions is the focus. Spin that fan too quickly, the air in the room mixes well, but the velocity may be objectionable from occupants. Slow the blades down, the air mixes more slowly, the occupants may not object.
Then it seems next to impossible to stir and mix unwanted low stratified cool air without causing an unwanted and cooling draft in the occupied area.
Not really. Especially if humidity is controlled well. In fact, a tight house will likely feel less "chilly" from the onset, so the fan on reverse may or may not be sought after. With that said, the trend is to build "great rooms" with giraffe-head height ceilings, which even with tight construction will present thermal challenges to the occupants. Maybe we should rethink interior space articulation, in that mile high ceilings ain't so great after all. Personally I find lower ceilings to give a room a more sheltering feel, and less of an exposed one.
True, moving air does not cool air temp but wind chill is real and calculable. Many variables would be used to determine wind chill factors. I would estimate that the very 5 degree rise that you are trying to achieve could be eliminated by wind chill factors.
ASHRAE's comfort index is more applicable in this scenario, since we're dealing with an indoor environment vs. an outdoor one.
Some of the smartest principles for heating are also the oldest…a fireplace. It creates no drafts, it allows the heat to gather on the ceiling while constantly removing the cold strata of air off the floor, it is quiet, it does not reheat your valuable heated air, temp transitions are without notice, and is both convective and radiant. But it has its own set of drawbacks.
Fireplaces are especially troublesome in tight construction if no provision for outdoor combustion air is made. They're not great in loose construction either, since they most often draw from the interior space, not from a dedicated outdoor air source. They can also be a hazard if not tended and maintained properly. I love an open, crackling fire like anyone may, but I never use my own fireplace, for it lacks provision to draw air from outdoors. Until that modification is made, the fireplace is a handsome architectural element, but little more.