Hi Musicman, welcome to iRV2.
You've come to the right place for answers.
It's good you are using GVWR's for the TT calculations - you are on the right track there. One thing to remember is the 7200 lb towing specs for your JGC is for a base vehicle, no options & only 1 150 lb driver. For everything you load into that JGC (wife, kids, gear, bikes, full gas tank...etc) you have to deduct that weight from the amount you can tow. My first impressions are that the 192 is outside of your tow vehicle's capacity, even though it's probably doubtful you'd load it up with the nearly 3700 lbs of stuff the brochure says you can put into that base model TT (also, that base model dry weight would not include things like a TV, awning, A/C, the water that sits in the hot water tank...etc. All those would add to the dry weigh specs listed in the brochure).
The best thing to do is to load your JGC with all people, gear, full tank of gas & head to the truck scales to get it weighed. Then take that loaded up weight & subtract it from your 12,200 GCWR to get what you can safely tow.
P.S. On edit, looking at the Forest River website, the Roos (or even the Shamrocks) appear to have many more models that would fall safely within your towing capabilities with more variety of floorplans (i.e. multiple bed options for you & the kids). That is, if you're not set on the Surveyors.