If the tower hasn't already been purchased, switch to an open tower. The two steps of heat transfer you propose (at the tower and at the HX)will be a real performance buster/energy waster.
If the tower is old, junk it and get a new open tower.
If its kinda old, consider scrapping the coil casing...
Perhaps your cooling tower is in need of repair which leads to excessive spitting. Get a good sales rep out there who can check the condition of your eliminators. Maybe someone tried to squeeze more capacity out of the tower by fooling with fan pitch, sheave size or something. Spitting is rarely...
Heat pump systems typically employ closed circuit cooling towers. If so, you don't have to worry about static lift- It's like a continuous pipe up to the roof and back. The bad news is the cooling tower probably won't be working. Even if it was, the flow would be laminar and thermal capacity...