Can confirm what OP is experiencing and also agree that it's highly annoying...
Basically the search zone jumps 2-300km away just a second before you hit the exclusion zone, coming in vertical (or steeply) isn't an option because you can't pull up in time to correct your course. Not sure if it depends on the planet or something, it's a real troll if intentional...
So yes, I think they could do with a tweak. They didn't used to be like this...
...I’m ok with chasing the wotsit around once past the exclusion zone though, especially in a fast ship!
That first big 'move' is intentional. It was added about a year ago, and in fact has been made shorter, at first it was always in the million meter range, last time I played (a while now) it was regularly just a few hundred km. I guess they realized that players did indeed feel trolled having to go back to SC because they dropped out just before it moved...
My guess is it was an attempt to make it more difficult or as others have suggested require skill, but IMO it's like much else in the game, predictable, meaning it's only even remotely challenging the first time (or two) you do it, after which, so long as you follow a procedure it's simply something in between where you are and where you need to be. In the case of the first move, it's simply a matter of going as slowly and shallowly as possible in orbital cruise, keeping the HUD target just visible, and when you see it get its 'spikes', you know it's going to move - usually when you are around 100km from it. That way you will still be in orbital cruise and it just adds a few seconds to the mission.
The rest of the moves are all small, and again they are predictable, coming once you get to within a few km of the target (well, the HUD marker). The last move always moves behind you so the target can spawn out of sight, and I do agree that it's perhaps a bit immersion breaking knowing you've literally flown right over where it suddenly appears only moments previously.
It's a shame that FD can't come up with a way to make finding things in the game more engaging, but I think the scale of the game makes that if not impossible, at least incredibly difficult, so we end up with lots of contrived challenge instead, which as I said, stops being challenging when you know how to approach it.