This looks like a paid position and I doubt they're going to accept paying me to promote my own site in any way. XD Hell, even if it wasn't a paid position, they'd still see us as competitors I'm sure.Cross-publish something you were already going to publish here?
Probably want you to do it for the "exposure".They explicitly say it's a volunteer position:
"This position is a strictly voluntary role. There will be no financial compensation from this position."