I would not move a large tank if I could possibly avoid it.
There are refugia marketed with powered in and passive out, but I don't remember who makes or markets it, those were short-term bookmarks and cleared when I decidied I was happier with using tanks.
The hazard to power in and passive out is overflow danger if the return is blocked or loses siphon. If I set such with the pump low in the display, I would have a float switch in the refugium (lower visibility, less obtrusive) or in the main tank (safest, but visible and not attractive) to shut down if the refugium were in danger of overflow, or if the display were lower than normal in water depth (depending on float placement).
I'm not certain that either of those mentioned is really large enough to make a significant impression on the green water issue.
Can we jump back to the original issue of green water a minute? Do you have a full-size hood and what is above your tank? What room is it in? The reason I ask is that emerse plants are more effective at removing nutrients from water than submerse, or than Daphnia at eating the resulting green water (suspended algae) and then the shrimp at eating Daphnia (although they can eat a lot). If there is space atop your tank, it is easy to set a tanktop W/D as a hydroponic plant tray, planted with Spathyphyllum (sp?) which would be more likely to alleviate the problem than all these too-small secondary processes - that would at least attack the primary issue. The Aquarium Products TT W/D that I used this way is about 5 1/2 x 5 1/2 x 48", only 36 of which is actually usable for growing plants. But I promise that is a huge mass of emerse plant and can absorb a lot of nutrient. If not, if there is space or possibility of a shelf above the tank, a balcony-type planter box could be rigged to serve the same function. The direct on the tank setup only requires a very small pump. Think about it.
A properly sized UV would kill the green water, but return all the nutrients to the tank - not as desirable as removing them.