Pentax, I'm afraid, doesn't really have anything comparable right now.Splitting hairs, but I don't think that's quite right. The medium-format 645D is a step above those you've cited (yet with a comparable price). And the recent K-1 (not to be confused with the K-01, nice job marketing guys) should be on par with the D810, etc. (see [1] and [2]). However, I'll grant that whatever else it might be doing with image quality, Pentax's autofocus systems have always been sub-par. They're improving, but so is the competition.
I'll defer to your experience with birds; I admit to being crappy with that. But I think in your example of capturing the ultimate instant, autofocus does not enter the picture (so to speak). If you're worried about the EVF delay, the (lack of) speed of autofocus will put you right out of the ballpark. If you want that decisive moment, you're going to need to be pre-focused. Or are you tracking the subject continuously? I have particularly bad results trying that.
The point I was attempt to make was that DSLRs are masters of flexibility ... if you can live with the size, weight and cost
And indeed, those latter issues are a big tradeoff, as the OP notes and I've found myself - since I got the Olympus I've hardly used the Pentax at all. You can't just wave them off as caveats, they really are important. If I'm willing to use the kit zoom lens, I can actually fit the thing into a pocket, which is a big part of why I bought it. As the saying goes, "the best camera is the one you have with you".
But it's not just availability, it's also handling and agility. The weight of, say, a 300mm equivalent lens on a m43 body is a small fraction of the same for full frame. That translates into better stability when forced to hand-hold, or ability to move faster onto target even when on a tripod, which is important when acquiring and tracking a moving subject.
On the other hand, that same thing is a detriment for portrait photography with a m43. The same geometry that works well for long lenses means that it's difficult to impossible to achieve the short depth of field that you can get with a bigger-sensor camera. I think Sony may have that covered, but for reasons we needn't get into here, Sony products aren't allowed in my house.
[1] DXO scores: K-1 is 96, D810 is 97 (https://www.dxomark.com/Cameras/Compare/Side-by-side/Pentax-... )
[2] "Image Quality is where the K-1 definitely outshines the majority of its competition at this price point, with the camera giving one of the best Raw dynamic range results we've ever seen, falling just short of the industry-leading Nikon D810. Low light Raw image quality is a match for just about anything on the market, falling just short of the class-leading Sony a7R II." (https://www.dpreview.com/reviews/pentax-k-1/10 )