You say "He doesn't seem phased by any consequences", but you only list, time outs, corner, "be gentle", and "gentle touch".
There are no firm consequences in that list. You need to be swift and firm after the FIRST time you warn him not to hit.
He's a male, and he's 3. Saying "gentle touch" is for babies. I've seen boys become downright violent toward their moms as they get older when they take the gentle, talking approach to things. I was at the park, and two 5 year old boys were fighting and being bad, and their moms were super, "Oh, sweetie, I know how you feel and blah blah say sorry blah blah." They were both like wild bulls, lying about who did what, yelling at their moms, and one kid blew up and smashed the park sign with his fist while his mom just prattled on all gentle style, like "OK, sweetie, let's go get your nap..." :-0 My best friend talks her son's ear off constantly about feelings-he literally beats on her at 6 years old, and has been since he was 4.
Get the book Back to Basics Discipline by Janet Campbell Matson. I have 3 non hitters from 2-5 years old. A little firmness goes a LOOOOONG way. Especially with boys. My son is 3, and would NOT try this. At three, if you don't get tough with him, he'll hit the wrong kid one day who will. He absolutely can communicate, this is nothing more than him "wanting to hit". You don't need to ban him from wrestling. He needs some nice manly rough housing. He can wrestle and not hit, you just need to be firm with him and make sure he does what you say. Get the book, at 3 years old, you're gonna need it! The fun is just starting.