Hi Dave - have you looked at the bridge cameras, such as the Fuji FZ series? They go out to 400mm-600mm, albeit with smaller sensors.
The Nikon P900 even goes out to a whopping 2000mm!!! 😱 Assuming you don't need large prints, this one may be a viable option. Just set it up on a small Gorillapod by your window, pre-focus on the bird feeder and trigger the shutter by using the Nikon ML-L3 remote. The Nikon P900 price is a little less than $600.
I'm actually considering the Nikon P900 myself, as well as the Fuji FZ series and the Sony RX10 III ( a VERY NICE option that goes out to 600mm, but at a daunting cost of $1500).
Good luck!!!
-Keith