I would gently pry the crack open, and then inject acetone (typically your local epoxy/fiberglass shop sells syringes).
I cannot agree with you here. Simply injecting acetone does nothing. Acetone is a solvent, it acts by dissolving and/or holding in suspension the contaminants you want to remove. But you must immediately wipe it away, or 30 seconds later the acetone has flashed, and the contaminants are re-deposited exactly where they were before. You can't wipe away acetone that you have injected into a crack.
The crack originally described in this thread may not have been contaminated with crud, but the teak oils will still be there. Minnewaska's crack, if it faces the sky, will doubtless be full of atmospheric crud as well as teak oil. Better to cleanly dremel out a crack and be able to get a putty knife wrapped in a thin rag in there splashed with acetone (or my new favourite, interlux solvent wash - flashes much more slowly) to properly clean the crack and actually remove the contaminants.
In the case of the problem originally described in this thread, unless you have pretty great woodworking skills and steady hands, opening up the crack with a dremel upside down from below would end up looking like a dog's @ss. So unless it is a huge drama to remove the piece, replacing it just makes more sense. I think in the long run, it would ikely take less time and frustration than any in-place repair would. Minnewaska's crack is facing up (I think?), so it might be more possible to do a passable job of opening up the crack to clean it out properly. A crack opened up and cleaned can be carefully filled with thickened epoxy. My recipe for thickener in places it will be seen is 2 parts teak flour (sanding dust) to one part West 404. Teak flour alone is too dark, almost dark chocolate when set up, 404 is too white. Together they make a very strong filler that when set up is pretty close to the finished teak colour.
The dutchman and butterfly patch methods you linked to are really great methods, but require rather advanced skills and good tools to come out not looking like the same dog's backside described above. Furthermore, doing those joints in place upside down in the case of the original post, would be a remarkable feat of both acrobatics and carpentry. I am going to do a dutchman repair in the cockpit coaming of my dock neighbours' boat, but it's a fairly large dutchman repair, about 2-1/2x8 inches so much easier. As well we will have all the time in the world to work the joint with a router and sharp chisels while debating the merits of real beer vs Bud Light with lime.
Minnewaska could consider a spline repair if the crack is long and kind of straight. That would involve setting up a jig so that you could use a router to cut a fresh clean square channel where the crack is, then make a spline out of a bit of teak to fit into the channel. Once the channel is solvent cleaned, West System is your best pal in the adhesive department. Glue in the spline, sand it flush, finish with varnish.