You have the right idea, but you will have to evaluate and figure out exactly what, if anything, needs to be adjusted.
There should already be a failsafe "stop" built in. The tumbler is usually designed so that, if the cock or tumbler shaft were to break, allowing the tumbler to swing around further than normal, then the back of the tumbler will hit the bridle and stop it from spinning. That's to keep the tumbler from swinging too far forward and allowing the mainspring to slip off the toe of the cam. If it slips off it can punch a hole through the bottom of the mortise.
So you may just need to check to see if the stop does or doesn't need to be built up a little.
On some locks this gap is a little too much, and needs to be built up. You check it by taking the cock off and carefully examining how far the tumbler will swing in relation to the mainspring on the toe. So long as the mainspring won't slip off, it's good.
There's one old reference book that many of us have used that suggests that the shoulder of the cock and this stop should hit at the same time. But that's not exactly right. You want to shoulder to hit first. And you only want the stop on the bridle to hit as a failsafe. So it's appropriate for there to be a gap as you see here when the lock in the rest position. You just need to check to be sure that it will indeed serve as a failsafe, as it's supposed to.
On some locks the shoulder on the cock will slowly wear the top of the plate a little. If the timing is too tight here, such that it doesn't leave a gap where the red arrow is pointing, then when that wear occurs in the plate, the tumbler and bridle will become the main thing stopping the forward travel of the cock. You don't want that. The bridle and tumbler are more fragile than the cock. So, the shoulder should be stopping the cock, and the failsafe should just be a failsafe.

I realize that you already know this, HighUintas, but just to round out the explanation, let me also say that when looking things over, check both the lower leaf arm and also the hook. You don't want the arm hanging over the edge of the plate with the cock in rest position. If it does, then it will punch the side of the mortise when you trip the sear. And of course you don't want the hook to slip off.

I apologize for editing this post several times. Just little hard to explain, I guess. I hope it's more or less clear now.