As you have discovered, SNATs & NATs apply only to load balanced traffic.
hoolio is, as usual, right on all counts.
I am wondering though why you can't use the external address and source NAT at the firewall, allowing only internally initiated requests for the external service ports in question? There should be no load balanced traffic sourced from the LTM selfIPs, just system requests like DNS, ssh/ftp outbound by an admin, that kind of stuff.
If you do want to go the external monitor route, this doc will be most helpful:
Click here
If you'd like to pursue this request: I just think it would be a good feature to extend the transparent health check type to make it possible to originate from specific IP address other than the self IP.you can open a case with F5 Support and request a CR (change request) be created (or there might already be a CR for it). This isn't a bad idea, so anyone who thinks it would be valuable, open a case to raise its visibility in Dev.
HTH
/deb