It might be too small for an HVAC person to take it on. It's somewhat hard to recommend because it does involve wiring, and perhaps some siding and flashing work. Many locales require electrical work to be done by a licensed electrician, and you don't want some bozo not doing the flashing correctly if they mess with your siding. You should be able to run the exhaust duct through the joist bays that make up the bathroom ceiling and through the rim of the cantilever. It could exhaust downwards out of the cantilever soffit, but that can sometimes not be the best choice. A small remodeling outfit might be well-versed all aspects of what you need to have done. A capable and conscientious handyman? That can be good or bad, depending on the person. Consider asking for, or use these as points within the conversation: -Rigid duct. Nothing "flex" or with ridges/corrugations. They can use a small section of flex to connect the fan housing to the run of rigid, but there should be no tight radii in the flex or any kinks in the flex. -All seams in the duct sealed with aluminum foil tape. Not "duct tape". -Insulation around the duct, at least within 4' of the rim. -Any horizontal runs in the duct will be pitched down for drainage in case the moist air produces condensate within the duct. -Ask how they will flash the damper into the siding of they run it through the rim. -Ask how they will damp the exhaust if they run it downwards through the cantilever soffit. -Consider getting a timer switch for the fan. You turn the shower light ON, the shower light and exhaust fan turn on. You finish showering and turn the shower light OFF, the light turns off immediately, but the fan continues to run for a time set by you; another 20 or 30 minutes. Do get an idea of how many feet of duct you'll need. Fans are rated to move a certain amount of air, the longer the run of duct and the more turns within that run, the more resistance to flow and the less air the fan can actually move. You might need to up-size the fan to actually move the needed amount of air.

Thanks for the suggestions. Text communication being what it is, I may have been misunderstood on a couple of points. The reason for not wanting to vent near the porch or under windows has nothing to do with appearance from the street, but rather what I thought was a more obvious objection to moisture and odor wafting in through open windows during the warmer months, or making the porch a less enticing place to relax or entertain when the bath is in use. I confess to being a bit fussy about details, so if I did go through the roof, I wanted the vent to be in the same line as the other two bath vents, which are a couple feet apart in the same shingle row, thus the offset in the attic. Another Q/A site suggests that the worst two places to vent a bath is 1) into the attic, even if under a ridge vent, and 2) under a vented soffit. The site "expert" instead recommends going through the roof, though the bath in this case is on the highest floor. The two existing baths have vented through the roof for many years with no apparent issues. The runs are relatively short, the duct is insulated and the vents themselves have dampers. Enough warmth seems to escape to keep snow clear around the vents. The clothes dryer also vents through the roof as the alternative would be to vent directly out to the front porch, which would create a nice steamy fog on cool days, not to mention the moisture rising up through the porch ceiling vents. Again, no apparent issues after years of use. Having said all of this, I appreciate the concern about running a duct from the basement to the roof. If I can find a path to an acceptable point along the rimjoist, I'll take it.

Brickeye thanks. For the record my statement on the neutrals all being tied together was incorrect. The load side of my GFCI feeds a protected outlet in that bath while that outlet feeds two protected GFCI outlets in a downstream master bath. The line side of the first GFCI is multipled to feed a fan and a ceiling light, and those neutrals on the line side (not load) are tied together. Nothing coming off the load side is multipled to non-protected devices. BTW the use of dielectric grease on that Broan QTR140 exhaust fan motor connector seems to have fixed the problem if their was leakage to ground. I still do not understand how moisture on what is now an unprotected fan (multipled on line not load side) causes the GFCI to trip. The load side is an entirely separate circuit. My original thread on this below is confusing because the tripping problem caused by the fan seemed to be fixed several times only to re-occur. Sealing the connector on the fan seems to be a cure for now. I wanted to tie up loose ends for others on these forums if appropriate. Here is a link that might be useful: Original thread on this

They sell smoke kits to test for things of this nature, problem that you're not thinking about is that smoke is naturally light and is easy moved from one location to another with the use of a fan. Heavy air, such as steam is not. Seeing steam vented could merely be only a portion of the steam vented from a room and due to exterior conditions being very cold in relation to the room that is vented. Just seeing steam vented isn't an indication of how much in proportion of what is in a room.