IMHO Pentax AF is not as poor as it's being claimed by a few here recently. That Pentax 55-300PLM might well be your solution.
Spent a few hours yesterday nestled in with a group of Canikoners at an airshow. My go-to was a *200 2.8 on a KS2. Lens of choice by the actual pros surrounding me there? Also either a 200 prime 2.8 or 70-200 2.8 which is supposedly way fast. Every single guy in the small group of maybe 5-6 near me used those lenses throughout the afternnon. The Nikon press guy who was carrying 4 bodies with assorted lenses told me his workhorse is still his 200 2.8. And of course there was the expected plethora of photogs below us with camo-wrapped bazookas who I guarantee missed out on a lot of shots with lenses that were just too long.
Had assorted aircraft (mostly jets today) in front of us flying lateral left to right, sometimes approaching from a 30-45 degree angle nearly straight at us, and a few coming from behind or directly at us/ overhead. Obviously many moving fast, Mach 1 and more. Other than those times where there was just a tad too much smoke in the air and had to goit manual I used AF.S or AF.C, and sometimes auto settings and sometimes program. Burst mode with most of the jet shots, single with the others.
For the most part I nailed focus AND my shot just as often as the Nikon press guy and one of the Canon pros I compared pics with (really nice guys too, dang helpful with advice and tips). At the end of the day I'd guess less than 10% of my shots were throwaways due to poor focus, maybe another 20% from just simply missing the shot. I'd call
at least two dozen absolute keepers out of my approx. 700 shots which by my standards is a pretty good day. I even caught two wonderful images (IMHO
) they themselves attempted but missed twice, so things around Pentax AF land aren't really as dire as some would like to convince you they are.
Just my .02
FWIW I asked the Nikon guy what he's recommend if I wanted a separate body just for sports and such. He told me D5200 or D300 which he said he buys used on eBay occasionally for $200-300 and watch for a used Nikkor 70-200 VR1 which he bought for under $700 a couple months ago. Or go even less with a 80-200 non VR. But still that's a grand or so and adds another body and OS to the mix that you'll need to learn.
BUT... Here's the big issue. Yes Canon and Nikon might have more advanced autofocus, but those comparisons are using recent (or relatively recent) models of those two compared to newer models of Pentax cameras. If you decide to buy a few years old model of anyone else's camera I doubt you're going to find much if any difference in AF performance between your current K3 and for instance an old D300.
If Pentax AF is factually at the level of two year old Nikon's (not agreeing it is) then wouldn't buying a 2014 or older model negate any advantages?
Personally I'd think putting a faster lens on the camera you already have and know is the wiser move.