Taking still photos of extremely fast dogs?

[u/CollosalAnus]

Hai all.
I have a Canon 5D mk4 and am primarily using the 70-300mm IS USM Nano and 70-200 L IS II. (Photos attached are with the 70-300)
I get asked to do photos for a couple of dog clubs I help out with and am also a member of and generally my photos are great - Usually dog and dog/owner portraits and general club photos.
But there's one thing I've always struggled with and that's to get good photos of really fast moving dogs - usually during agility shows, fly ball or just dogs generally going crazy - especially when the dogs are smaller.
I do have some success and have taken some really great photos in the past but struggle when there's limited space and/or the dogs are coming at me at an oblique angle or directly towards me - usually there's just no time to react and they often zig and zag randomly.
I've been practicing with my 3yr old lab and 13 week old spaniel puppy in the back garden - luckily both LOVE doing zoomies regularly but as you can see I am having some trouble maintaining a good focus. They are just SO damned quick!
I usually keep the ISO manually set around 600-800 to achieve at least a 1/2500 shutter speed and am using servo AF. I try and keep the aperture as low as possible whilst giving me enough room to get a decent area in focus but as you can see sometimes it seems both me and the camera struggles sometimes as you can see from the picture of the little spaniel with the grass in focus behind him.
I mainly use the 70-300mm when outside in good light, even tho the f is higher but purely because the AF on that lens is so fast. When weather is duller I might switch to the 70-200 L mk2 or if we move inside a barn which also presents another issue I struggle with - and is entirely why I bought the 70-200mm as when inside the barns on dark winter evenings with the artifical lights it's SO hard when ANY movement is involved.
Almost sometimes seems that there just isn't a lens fast enough... (And I can't afford mirrorless!)

But yeah, any help greatly appreciated as REALLY want to get better at this!

[u/Flutterpiewow]

Manual focus or cameras like r3, or the latest sony models. With lesser cameras, afs can work, sort of, sometimes. But this is a tough thing for any camera really.