So, first, that is not supposed to be done due to the potential of a reverse draft turning the air intake into a chimney. It's not your fault, the manual is deficient in not pointing this out. Most stove manuals have a specific caveat stated in this regard. Detach it temporarily to see if this is an issue affecting draft.The Airintake outlet (where it goes through the wall) is approximately 5ft above where the vent goes into the stove.
Secondly, if the wood is dry, this really sounds like a draft issue. The stove should be connected to a 6" r flue. (~28 sq in). Draft is getting reduced quite a bit by the 3' horizontal run. Changing that will help if the horizontal run can be eliminated by using 45s and an offset. But it still may need a 6" liner in the chimney.