Is this even possible? (~7 second audio delay)

Well Chan describes in the list of effects the most basic one - delay. Which does what you want, I think - it delays the input. Of course in the context of his article it is about sound effects.
I think that a cheap (old, off ebay) laptop with Linux can do the job, after some time spent configuring some software. There are plenty of options: List of Linux audio software - Wikipedia