I started writing this before the crunch came in Post 6, and will continue on that basis, as others might be in the same situation.
As you lift the blade out of the scales? That suggests to me that there is enough movement in the crack and/or the scale to collar joint, to get a little superglue in there by capillary action. It is about the only glue that I think will do that (if you use the cheapo, non-gel grade). It is true, it will stick to some plastics but not to others. Still, I think it would at least reduce the appearance of the crack.
It is a pity that we use the word "celluloid" loosely nowadays, when it is properly applied only to a plastic made primarily from cellulose nitrate, which is very little used nowadays. It is quite easily glued (as in film splicing), or attacked by numerous solvents whether you want it to be or not. IF this was true celluloid, I would consider dismantling the razor, coating all the exterior areas of the scale with tape, and introducing acetone or (perhaps better) amyl acetate or ethyl acetate) into the crack from the side which would normally be concealed. If they get on exposed surfaces, there would probably be frosting to be polished away. Thinned clear nail varnish might be even better. I have an idea most nail varnish removers, although primarily acetone, may include an oily substance to reduce embrittlement of the nails.
I would be very reluctant to replace these scales if I could get out of it. I agree they don't look like ivory (though it is always a pity to give someone an unwelcome opinion), but they are attractive, original to this razor, and hard to reproduce with the original transfer or inlay. I'm guessing about how the logo was applied, but it may have been aluminium held inside a mould into which the plastic was injected. Or it could be metal-impregnated plastic, and likely to disintegrate under any kind of treatment that will get it out and in somewhere else. If it is on the surface rather than inlaid, I think it is as likely to be paint as a transfer.
I would also have considered drilling a tiny hole or two into the end of the scale, through the crack, and inserting pins made from thin piano wire. Ace Hardware made an off-white epoxy (and an equivalent must be available elsewhere, for bathroom fittings) to fill in the ends of the holes.
The other side of the scale breaking is not entirely a negative development. If you are resolved to replacing the scales, nothing you try first is going to lose them for you. You can clean away any traces of oil which had got into the crack, and you can use any kind of glue you like. You can use the hidden surface where the broken-off piece used to contact the blade, to test tiny globules on a pin-point, and see if they adhere. Between cyanoacrylate, acetone, plastic model-making cement and epoxy, there is a good chance something will do. You can also see whether that lovely warm hue is applied by staining (which would necessitate very careful polishing afterwards), or all the way through the scale.
Are there thin friction washers between the scale and the blade? Even if there aren't, one made and glued to the scale would strengthen any joint. Tattoo machine shim washers (e.g.
100 Brass washers to shim your tattoo coils 10 sizes | eBay ) look promising, but I would probably paint one on a piece of single-edged safety razor blade or industrial package strapping strip, and etch it out with acid.
Here is a link to some horn I have just received via eBay. The seller seems very reliable, and his other horn and bone bears looking into.
Large Flat Dark Horn Blank Plate 160 x 60 x 5 mm | eBay My first purchase from him involved the export of camel bone to Saudi Arabia, which must be something of a commercial milestone. So Australia ought to be pretty run-or-the-mill to him. I am pretty sure the buffalo are domestic, which unlike ivory places them outside CITES controls.