I agree with the others who've answered before me. If there's a way to change any of the 90 deg. stuff to a couple of 45's, that'll help. A little. The "wet" wood is a problem. Less BTU output, poorer draft, more creosote. However, perhaps that is just what you must work with.
After ten yr. of using the inexpensive black pipe, I installed the double-walled, insulated stainless. It is pricey. And the "accessories" [caps, etc.] are as well, and the regular ol' sheet metal stuff won't fit. It is heavy, so must be supported. My outdoor portion of the pipe is tall and I've got it secured by guy wires for wind protection.
The sections lock together in a screw-type motion, so that would probably cure the smoking indoors.
Around here, the only places to get this stuff is through building supply companies, and not your quintessential big-box supposedly discount chains. That means more money.
However, we've been using ours for around 25 yr. and so far there is no problem. The cost made me gulp, but I've had very little maintenance on it since installation. With the black pipe, I had to clean it out a couple times a winter and replace various sections every couple years.
But you need to think hard about some way to alter the pipe run, in your case, if at all possible. Maybe a 45 to the section thru the wall, then another 45 to transition back to vertical. If you can get rid of those 90's, it'll be a start. If you get smoke back in the house, you are also certainly getting carbon monoxide.