The modern-era Nikon 1.4x, 1.7x and 2x autofocus TC's are incompatible with the rear element design of the 80-400. The only Nikon TC's you can use on the 80-400 are the older,manual focus-era TCs like the TC-200 or TC-201. The rear element of the 80-400 is very far back in the barrel and the front elements of the Nikon autofocus teleconverters will cause "crash n bash" on the 80-400. You'd have to look into a Kenko TC to use on the 80-400. I have an 80-400 and have can verify that the Autofocus Nikon brand converters are not physically able to mount to the 80-400, even if you mill off the safety tab...
Like icassell says, the options at this range are not cheap...there is simply not much middle of the road in the above 400mm length...
Cheapest option in Nikon is to scrounge up a 600mm f/5.6 ED-IF Nikkor, or the 500mm f/4 P Nikkor manual focus lenses, or buy a 400/3.5 ED-IF Nikkor and a TC-300 or TC-301 (both 2x converters) and get an 800mm f/7 with the 2x attached. That has pretty decent quality for maybe $1300-$1600 total outlay. Sigma 500mm f/4.5 AF lenses are available in the $2k range used.