Well, yes, actually a second IP address could work. That's how web sites worked before SNI was implemented. You'd have a server process per site, listening on its own IP address, each with its own configuration file, pointing to a separate SSL certificate.
And you could do that with Exim: have a separate Exim configuration per IP address, each serving a particular domain, and with its own SSL cert. But it's probably easier to hack the Exim configuration to use SNI. Exim does support SNI, so it is feasible. It's just that we've not tried it with Symbiosis.