Hi,
My apologies for not responding sooner - I somehow missed this!
OK, so what you are trying to do is a kind of "reverse-bullseye" where we are expanding the set of valid interactions as opposed to expanding the set of valid agents.
I have had a bit of a poke around and I think I may have a line you could investigate. (Note, I have NOT tested any of this out and it MAY not work, so use at your own risk!)
In a nutshell, I think you need to use ACD Categories. What I believe you want to do is to assign a category (let's say, you name it "email") to all incoming emails. (ACD Tab->ACD Specify Interaction Category). Then when an agent becomes available, make sure they do not have that category. Start a timer and after the required delay, check if they are still available. If they are, assign the category to them (ACD Tab->ACD Agent Category).
Emails will then only go to agents who have the category, which should only be those who have been available for more than the required time. (Note, if there are no interactions waiting at all, the agent is sat waiting and then an email comes in, they would get it immediately).
I'm fairly sure that with these tools, you can get something working. Let us know how you get on!
HTH