Yep, I have the same setup though my kettle is the Bonavita.
What I found was the same; that the last bit takes a long time to drain.
What I also discovered was that the grinds tend to ride up the sides into the flutes of the filter. If you try to rinse them, it make the slow drain at the end even worse. I've not perfected using the brewer, but I would make the following recommendations:
1) don't try to brew a large amount, I think with less grounds in the basket will be less problematic.
2) don't try to rinse the fluted (folds) part of the filter if coffee grinds stick into that area.
3) what worked best for me was to pour all of the water into basket fairly rapidly (rather than small additions over a longer period of time) high enough to get good saturation of the grounds and let it do what it does. This seemed to produce the best cup for my palate and minimized the slow drain issue, and I had no more water to tempt me to rinse the flutes.
Share your thoughts on this too. I think a non-fluted filter would work better... the filters have large flutes.
TD
I assumed those large flutes helped with draining. They certainly create more surface area for the wet grinds to stick to (i.e., if there were no flutes, much less surface area, and potentially even slower draining).
At first I was "rinsing down" the grounds that were clinging to the sides of the filter, but then I realized it was probably better to leave them there. Since the water additions will flow through the walls of the filter, I wanted to leave grounds on the walls so I got the best extraction. No more rinsing filter walls for me.