Rob,
I have a similar vent setup on my Enviro.
Out the back of the stove to a clean out "T" then straight up through the roof to a termination cap.
All of it 3"
I use a vent brush similar to a lint eater. Has a round set of bristles on a flexible PVC type plastic shaft that is about 1/4"-3/8" thick and about 10' long.
The brush works well for me.
What I do is to remove the vent from the stove at the T. Then pull off the fist 2 inside sections to just before the cathedral ceiling box.
I take those outside and run the brush through them until clean.
I go back in and while standing on a ladder, run the ash-vac (Shop Vac) with the hose sucking at the lower lip of the ceiling vent.
I then slowly run the brush up and down the vent, sucking up all the debris that falls down.
This gets about 95% of it.
The vac does a great job of catching it.
The rest I just vac up around the stove and hearth.
In the spring I pull off the term cap and clean that with compressed air.
Other Ideas....
Do you have an OAK? If so, is that blocked?
Could it be your pellets?
You might want to try a few bags of Ultra Premium, Super Whamo-dine, Works Great-Lasts a long time-Drains to the bilge pellets
(Or whatever the PFI is calling good pellets these days) to see if there is a difference.
Good Luck,
---Nailer---