Have very specific posting campaigns for the other forum....and pay users here to post on the other forum to generate traffic here.
E.g., the AMA series is a brilliant idea - one that a significant volume of people would be interested in but only a handful of people on the other forum are aware of. Set up a targeted campaign to get members here to post over there, advertising events taking place here.
Keep the campaigns short in duration - one or two weeks each.
Measure activity following the campaign.
Pay people to make the posts...which in turn generates another kind of loyalty to drive rankings and SEO placement.