Is it possible to specify both a RSA-SHA1 cert and a RSA-SHA256 cert that way, or would it have to be RSA-SHA1 and ECDH-SHA256?

Apache/OpenSSL would have to assume that pre-TLSv1.2 clients support only SHA1 because there's no signature_algorithms extension, but for TLSv1.2 clients can Apache/OpenSSL choose between a RSA-SHA1 cert and a RSA-SHA256 cert?

The reason I ask is because ECDH certs seem to be even harder to come by than RSA-SHA256 certs right now.

I haven't tried, but I think at the moment Apache supports only multiple certificates with different private key algorithms. Anything else would have to be implemented in custom code. IIRC, OpenSSL 1.0.2 (not yet released) has better support for multiple certificate chains on the same server.