You probably want metal barrier layers inbetween. Except you don't...
I'm thinking HV diodes (a single part, containing a stack of matched single diodes, to achieve the required rating) are common dies simply soldered together. You could shorten the process one step by using aluminum layers between N/P layers. But, then your crystal structure gets screwed up, and you can't keep growing single crystal. So, obviously that's not a useful method.
I think a heavily doped layer will work, to a point: you get a tunnel junction, with a very low breakdown voltage. It's not ohmic, but you probably don't care at this point. But there's nothing to stop carrier diffusion, so the result is a huge stack of DIACs, which I don't think will work very well.
Maybe you can grow the heavily-doped regions very thick (10s of um), so diffusion and recombination kills off the thyristor gain?
Stacked single junctions also can be tested individually before assembly.
(It's been some years since I've practiced theoretical semiconductors, so this is probably stuff you already know better about.)
Tim