"Gmail has a reply all button and a forward button"
Last I checked, neither of those buttons are designed to publish the whole conversation to the whole world via the World Wide Web. Your product is. Therefore:
"we're changing the product to make it possible to upload stuff without permission"
Then you're changing the product in a way that is absolutely unacceptable for privacy reasons.
"we're not trying to induce bad behavior"
I'm not trying to induce meth addiction; I'm just selling it and hoping it won't be abused.
"And for the most part it works, since there are only so many times you can abuse those features before people stop sending you emails."
Then you're missing the point: I want to minimize the potential for abuse to ever happen in the first place. Hence the ultimatum in my top-level comment: if I know someone is using this service, then I'm going to refuse to communicate with that person via implicitly/semantically-private channels (in fact, it'd be nice if there were some way to programmatically get a list of email addresses registered with this service so I can maintain a blacklist on my SMTP servers and prevent myself from sending anything to them by accident). I might waver from that if FWD:Everyone offers the ability to preemptively register my email address(es) in an "automatically deny permission" list.
"There are many times when it's easy to get verbal permission from someone, but difficult or impossible to get email permission, e.g. if their email address has changed."
Then that request for verbal permission should be along the lines of "hey, I want to post our conversation from a while back to FWD:Everyone; do you mind logging in real quick and approving it since the request probably went to your old email?". Even better if FWD:Everyone would keep track of who owns what emails and send requests to alternate emails if not approved in a certain amount of time.
Otherwise, tough beans. Just because Disney didn't respond to my email asking for permission to sell bootleg copies of Frozen on the black market (e.g. because I sent it to the wrong address or because it's obviously going to be a "no") doesn't mean I'm automatically allowed to do so.
In other words: if I'm unable to provide consent, then assume that I do not consent. Inconvenient, sure, but that ain't my problem.