Just a few comments.... first, I had 2 copies of the 120-400 and sent them both back. Like the Sigma 70-300 which I also still own, they were just too soft at the long end to pay for. Also, a, TC ( Teleconverter) makes it very difficult for an F4 lens to focus in low light... or even average light. My F4 60-250 with a the 1.7 TC is F 6.7 wide open, and that definitely isn't optimal for the K-5. Given that I bought the 60-250, you don't really notice 50 mm all that much. If you have the 60-250 you probably don't need a 300mm lens. You just don't get that much more. SO, if you plan to use a TC, I'd definitely go with the Tamron 70-200 2.8. That extra light is huge for efficient auto-focus when using a TC on a K-5.
Another consideration... in my opinion, even the 120-400 that I sent back was probably better than the DA* with a TC. SO if you are going to get one lens for birding, For me it would be the 50-500 or the 150-500, which ever is sharper.
Another consideration here is that if you were shooting FF, you'd be probably cropping within the APS-c sensor size anyway.. how is this important? 500mm APS-c is likely to give you the same final images as 500 mm FF. The usual crop factor won't apply unless the FF image is the same MP as the APS-c image. So , the equivalency conversion, 500 mm APS-c = 750 mm FF may or may not apply. If you're comparing with a 24 mp FF system, your images will be exactly the same size and the whole FF equivalency thing is off the table.
SO I guess what I'm saying is.... the more reach the better, don't depend on a TC to boost your image and maintain IQ.. Pentax has a 560 mm lens on it's roadmap that is probably closest to what you want, but who knows how much that will cost.
ANyway... a few shots for your inspiration..
Close in , any lens will do.. this one from about 10 feet away. When I shoot the birds at my bird feeder, even so-so lenses give me good images.
From a distance, you don't want to be using a TC, or a cheaper lens. Their lack of resolving power is more noticeable for shots taken from a distance.
As much as I've grown to be leery of Sigma lenses, one of the ones that goes to 500mm is probably going to work out best for you.