Please let me know if you have a recommendation for which cryptographic algorithm I should use or if you know or if you can think of a more elegant solution.
I thought of a simpler way to force divergent balances to be incompatible while still retaining transaction protocol compatibility. Treazant will first copy the wallet and synchronize to block 109,999 without transmitting transactions. For each public/private key pair address that contains bitcoins, two new public/private keys will be generated. Both Bitcoin and Treazant will get a copy of both new addresses, but the treazants and bitcoins will be sent to opposite addresses. Neither the kludgy double signing idea nor the alternative encryption idea will be used.
this means I can double-spend my bitcoins on both chains, treazant and bitcoin?
Yes, you will be able to double spend Bitcoins/Treazants which you had before the first Bitcoin four year reward halving occurred at block 210,000. Don't delete your transaction history from when the Bitcoin reward halving occurred and I'll let everyone know when treazants are usable and worth more than nothing.