The math is correct. If p = the private key, P = the public key and G = the base point of the EC crypto system then P = p(G) where p(G) is the scalar multiplication of p selected from the finite field used to generate the elliptical group with the base point G from the group.
So for any two key pairs: P0/p0 and P1/p1
P0 = p0(G)
P1 = p1(G)
P0 + P1 = p0(G) + p1(G) = (p0 + p1)(G)
So you can take two public keys and apply the defined elliptical group addition and the resulting public key will have the corresponding private key which it the simple modulus addition of the two private keys.
That should work, I had completely forgotten you could add two points together, I only remembered about scalar multiplication. A light bulb popped up when I remembered point doubling was the basis of the whole thing.
The two parties could generate a signature to each other to prove that they possess the secret part or use any secure channel.