Looking at the JLink, it should work. Let me know if it does.
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.