I shoot a lot of wildlife so reach is very important. Maybe the best way to answer your question is to recount my journey.
I started with a D7000 and a D90 in 2011 and quickly started leaning towards wildlife and birds in particular. I wanted to upgrade after 18 months or so and had to decide between the D7100 (more MPs) or the D800 which had more MPs in full frame and the same 16MPs as my D7000 in DX mode. I opted for the D800. Big mistake. Long story short, shooting in full frame made for HUGE raw files that quickly filled my hard drive even though I was cropping out huge portions of them, but I found shooting in DX mode almost impossible because the viewfinder doesn't change, you only get a box in the center that you have to keep your subject in - easy for anything standing still but a major PITA for birds in flight, of which I shot a lot. After 9 months I bought a refurb D7100, converted the D800 to infrared, and was happy as a lark.
I own a D610, D750, and a pair of D500's. The D500's are my wildlife cameras, period. I see what I'm shooting and it adds 50% to my reach. A Teleconverter fixes nothing, and could diminish both image quality and focus ability (that said, I regularly add a 1.4x to my 300mm with good results). If I'm shooting wildlife with a DSLR I will always shoot with a cropped sensor camera. It's obvious some of the people above don't agree with me, but I'd never call moving to a DX a "step down". There's a right tool for every job, which is why you don't see roofers swinging framing hammers (not that you see a roofer actually swing a hammer any more). The guy stressing the noise difference between the D750 and D500 is right to some extent (it's about 1 full stop "worse), but he's getting 9.6MPs in the area I'm shooting 20MPs, so who do you think is going to get enough of that bird in a bush to have a photo that they have to worry about noise in to begin with?
Since you're shooting with a D800, if you picked any of the D7xxx cameras currently produced you'd get a pretty significant bump in megapixels over the D800 in cropped mode, and more MP's give you more pixels per bird so cropping in would be improved. A D500 gives you less of a bump (16MP to 20MP) but you get more FPS and a greatly improved focusing system. Either way, for wildlife a cropped sensor camera would (IMHO) be a step up from what you have. The TC will help but only on a subset of lenses so make sure you check before trying. They're another tool, but not a miracle cure.
That said, I am waiting for the next full frame mirrorless with great anticipation. I'm expecting over 50MP which means that it will at least match the 20MP I get from my D500. But the huge plus with mirrorless cameras is that when you switch into DX mode the electronic viewfinder zooms in so that it still fills the eyepiece - the one major stumbling block I had with the D800 and other full frame cameras in cropped sensor mode.
My 2 cents.