pegleg wrote:
If it's just an attic, why do anything? Our house is similar: stove and
both bathrooms vent into an attic space. It adds a little moisture, but
that's about all.


This is a code violation just about everywhere and for good reason.
Putting moisture into a cold attic in most climates is a prescription
for disaster. The water condenses and leads to rot and mold problems.
There have been plenty of threads in here with people having these
problems from improper venting into the attic.

For the OP, it sounds like a roof vent is the way to go. 20ft to the
side wall is too far to get any decent air flow. While you may be
able to share the existing roof vent, I tend to doubt this will meet
the code reqts, so you may want to consider that.