A tough assignment!
Your perfect lens would be something like the Canon 400mm f/2.8 IS or 500mm f/4 IS or the Nikon 200-400mm f/4 AS - none of them available in Pentax mount, and any one of the three around about the same price as a brand new 4 cylinder car.
The work you are doing seems to me to be crying out for three things:
* a) Fast glass - f/2.8 or at least f/4
* b) Image stabilisation
* c) High ISOs
Pentax don't seem to have joined the IS trend yet, and the third-party makers are dragging their feet on this too: very few lenses from Sigma et al have IS. Is it possible Pentax will do something Minolta-fashion with the new bodies due out shortly?
Nor are the current Pentax cameras regarded as good for high ISO work, but this too may change shortly. Canon have long been the kings of high ISO but the latest Nikon isn't all that far behind, and it's a reasonable bet that the next Pentax release will make a lot of progress beyond the elderly *ist lineup.
Pentax do however, make a lens that looks as though it could be just what you need, so long as you can manage without IS: the 300mm f/2.8. Long enough to give you a rough chance of getting a bird to fill the frame, and wonderfully fast. Alas, I imagine it is quite expensive. Worth investigating though.
300mm is really too short for bird work, but few of us can afford a 400mm f/2.8, and fewer still can happily face the thought of lugging something that heavy around all day. You have some tough choices ahead of you!
One last thought: teleconverters are better than a last resort, but not much better. Almost all the time, in poor light, you will get better picture quality by leaving the TC in your bag and shooting with just the bare lens. Even in good light, you are sacrificing quality: my 1.4 converter, for example, has 5 extra bits of glass to add on to the lens itself, the 2X converter 7 elements. Every extra bit of glass costs you image quality. Some won't agree with me, but I think it is madness to buy a lens planning to on using a converter with it as routine. Buy a lens that's long enough to do the job in the first place. Yes, it will cost you more money, but better to spend $3000 than waste $2000. And f/6.7 just won't cut the mustard in the sort of light you are talking about. F/5.6 strikes me as a bare minimum, and f/4 much more usable.
Yes, one extra stop makes a very real difference! The moment I see my shutter speeds dropping below 1/1000th of a second, I either swap lenses (if I'm using the 100-400 f/5.6) or take the TC off (if I'm using the big f/4). It really does make the difference between good shots and yet more blurry throwaway frames.
The long and the short of it: I think you have to plan on spending a bit more than you are hoping for. Good luck with your quest and let us know how you go!