So here's my experience of venting through the soffit. The humid air from the bathroom is expelled downward and rises up again to the soffit and in very cold weather in Canada it freezes there, then melts the next time the fan is used and eventually over time it seeps into the wall and runs down. In this situation there is aluminum soffit over the old wood one and I guess it runs down on the wood. There is also considerable ice buildup on the roof above the vent forming an ice dam. This method of venting might work for warmer climes but beware using it in areas of prolonged cold.
I presume the question is: What can I do about this situation?
I don’t live in such a severe environment and have not considered such extreme conditions, but it seems like you’ve got a couple options: 1) deflect the exhaust away, 2) increase volume to move exhaust away,
1) I’d look at your exhaust grille in the soffit. Most have blades that angle. If the angle is turned towards the house, I’d rotate them so they “push” the air away from the house.
Perhaps a custom made sheetmetal deflector could be fabricated to help deflect the air too.
2) Additional volume of air could help deflect the air away from the soffit and eliminate the stagnant air at the grille.