We want to add a system to allow people to get in touch with each other outside of the forums. Many people aren't happy to make their email address publicly visible, so we need an alternative.
Typical forums offer Private Messaging, but lots of people find these somewhat frustrating - yet another thing to check, learn to use, etc.
There are several alternatives:
I'd go for no 2.
I'd say no 1, similar to Pprune if you set your options there to email delivery. Works.
1 or 2 seem fine to me.
Not wishing to influence the vote but please carefully consider what you actually expect of the system, rather than what you have used previously on other sites.
Just forwarding your message as an email, and allowing subsequent comms to be done directly between you, not involving this site at all, reveals your identity to the recipient (unless your email address is obscure).
The big Q is how many people actually care about that i.e. sending someone an off-forum message and remaining anonymous to that person. I think this requirement is rare. Let's face it, it would be bad manners to do that with a phone call, or by email. On another site, years ago, I did once get an extremely handy tip from somebody who clearly wanted to be (and was) totally anonymous, but that is the only occassion I recall from the last ~10 years.
A full "private messaging" facility, with all the mailboxes, etc, protects the original sensor's identity but has a number of downsides which include:
Taking on board your comprehensive points I'd say that option 2 is just as valid.
But I rarely PM and just as rarely have it done to me.
Whatever you feel is appropriate. It's not a deal breaker for me.