I would switch from free feeding to scheduled as a first step. I feed 3x a day. Early in the AM while I get ready for work, when I get home from work, and shortly before bedtime (and MowMow gets a 4th meal of raw beef JUST before I go to bed to up his calorie intake). Two meals per day is usually just fine. I enjoy that third meal because once they eat, they groom then go to bed and are quiet for the night.
Once they are accustomed to scheduled feedings you can start switching them to wet.
I would probably do it one meal at a time... a few weeks later switch the second meal to wet.... another few weeks switch the last meal.
I feed a grain free canned diet to my 3 boys. I have a bunch that I cycle through so they don't eat the same thing for more than a month at a time (and I feed two kinds each month).
Hound & Gato
Evangers (when money is tight, but make sure the label says it's complete. Some of their food is NOT complete and needs to be fed with something else)
Merrick (this has to be watched, it was just sold to Nestle so the sourcing may become questionable at some point)
Addicton (If they'll eat it, my boys won't eat the raw or the canned)
Most mom and pop stores will offer these by the can to test (I test for 3 or 4 days... just 'cause mine will eat it once doesn't mean they'll eat something the 3rd or 4th time it's offered). It stinks to buy a whole case and find out on day 4 they now hate it and would rather starve to death than eat it.
Mom and Pop stores will also usually offer by the case discounts once you find some the cats really love. My local store let's you mix and match a case so if they have tons of grain free brands you could get a case of mixed cans to try lots out at once with the case discount.