All depends what you mean by “nearly instantaneous.”I explained exactly what I meant, in some detail.
And yes, in my case and in my group, and no doubt in others, there areWould this work for you? In those cases where, upon reading the "Message Approval Needed" notice, you begin a non-instantaneous process (that is, you do something other than immediately accept or reject) you could step through to the Pending list on site and claim that message.
Or, maybe part of this suggestion (or a separate #suggestion) should be to add a "Claim this message" link to the Message Approval Needed notice, akin to the existing Reject and Delete links. That would cover the case of moderators who can't or don't want to go on site.
Now your process can proceed in a protected fashion. Which, I think, is what you have asked for - a means to avoid investing time in a response only to have the message disappear (be accepted/rejected by someone else) in the meantime.
You can’t wish the problem away.No, but I can suggest means to minimize the problem (other than by investing the site with the clairvoyance to know that you're considering a message off line).