I use a BBQ professionally and cook on them for up to 40+ people weekly. Wild rabbit saddle is acceptable barbequed but any other part is tough. Had similar results wild foul, even cooked young Canada's just flying, still tough, but acceptable. I don't mind tough meat and am especially fond of Wood pigeon pan fried but BBQ seems to make non fatty meat tougher and most wild game is non fatty.
The marinade may be the answer so I will it and update you when I have, although I have used marinades before.
Anyone else had good results barbequing rabbit?