(reply EDITED after a good night’s sleep)
I can see why you’re concerned. It sounds like this started out small and is getting longer with each successive fire. Have I got that right?
You are better off with one of the refractory silicone products than trying more mortar. Rutland Red is one example. I used this DAP product in my oven interior because of its high-heat qualities.
For your application I’d much prefer that to chiseling out anything — once you start, you’re not going to be able to stop easily and you risk breaking more brick. Since that’s at the base of your opening, it’s supporting all the weight of the brick, the mortar, and the lintel piece above.
It did that because the structure is settling. It may have a little more shifting around to do, but that’s likely to be the end of it. Patch it for your own peace of mind, and install your door, but don’t break any of that brick.