After all the threads I've read on this topic, the only one I'd currently recommend for you would be the DA*300 and 1.4 TC, or the DFA 150-450.
My own choice is Tamron AF SP 300 2.8 as my heavy lens. With it I use the 1.4 TC for 420mm ƒ4 or the F 1.7x AF adapter, 510mm ƒ4.5
For my lightweight option, I use the DA*200 2.8 with both adapters, 280mm ƒ4 or 340mm ƒ4.5, or stacked 476mm ƒ6.3.
The 1.4 will vignette and requires cropping, but that's not an issue with most long glass images. Your K-1 will give you 30 MP instead of 36 MP at worst, sometimes the vignetting is not noticeable.
That'w where I've ended up. On the way, I've used a Sigma 70-300, a Sigma, 120-400, an A-400, and my DA*60-250, my F 70-210 and an FA 28-200.
None of those options give me what I'm getting now.
And I bought a Pentax XG-1 instead of the Panasonic FZ2000 mentioned above for $200 and in good light it gets me to 1250mm equivalent. That's the inexpensive way to go if you can find one second hand.
Pentax XG-1, 1250mm equivalent, at 500 meters (close to 2 football fields away).