Hi Treebeard,
As others already mentioned, there are wireless kits from various manufacturers (niles, sunfire, etc.) that you can use with virtually any sub, so that may well be a better option than trying to find a dedicated wireless sub as you’ll have much more choices in brands and models.
With your Velodyne being the bane of your wife’s existence (had a good laugh at that one :)), I would say that your best best would be to go with a compact, high excursion sub like the Sunfire HRS12, Definitive Technology Supercube 6000, and JL E112 (a bit above your target price range, but a good option nonetheless) and pair it with one of the aforementioned wireless kits. These are the closest to your price range that I can think of off the top of my head.
I own an A/V integration company in Atlanta and would be happy to assist you further if you have any additional questions - I’ll send you a PM with our contact info.
Take care,
-David