It sounds like I have a similar setup to what you have, though I am venting out a basement window. I have the option of cutting a dryer vent, and you might as well- which is probably the way to go. You could also try and add a damper to your vent, I don’t think it would be an issue, but that is definitely not my area of expertise.
Anyway, because of the longer run, I definitely recommend a booster fan. I am using one that was around $30 from Amazon, called a “Vivosun”. Once I added this fan, a lot of my odor issues went away. Here is a thread that I wrote up on it, and it has links as well.