I would design in some more clearance than 3-4mm from crucible to furnace ceiling. I would probably try an A2 or A3 until you think the unit is proven worthy of a chopped A4. PS If I HAD to...I would chop one on a wet tile saw, shimming the small end while cutting the big end. Dry it off, let it air dry, then dry-fire it slowly to remove any moisture from cutting. That worked well for my plinth.
3/8-1/2" or 1-1.3cm is where I would start, keeping in mind you need to lift the crucible and pull it out, full of heavy molten metal, from the front if I remember correctly. Shimming- Since the table of a wet saw is flat and the blade is perpendicular, the natural 'lay' of the tapered crucible will be an odd angle to the blade. If you 'shim' the crucible on the side at the bottom, the top edge of the crucible should become (more) parallel to the blade, making a nicer cut. Rotate and repeat until the cut is complete.
Thanks again for the link for the ladle wash .. I've be using a kiln shelf wash to coat the inside and outside of my crucible.. Picked it up at a ceramic supply store.. Think it's mostly kaolin clay.. I use empty 1 pound propane bottles.. The fat green ones.. I get 4-5 melts if I recoat after melting.. About 2 lbs.. I'll try adding a little sodium silicate to the wash next time.. I can see why that would add a little extra grip on the metal crucible.. Was even thinking maybe a tiny drop of Dawn dish soap..