Hmm rib eye is a more a "medium" otherwise it's a bit lacking as you say, anything with loads of fat I tend to cook a little longer just to ensure it melts through and get it really charred on the outside, it gives a lovely, deep flavour. By contrast, fillet I'll each pretty much raw.
Deffo recommend a boned leg of lamb for the BBQ though, it worked extremely well. Thank heavens for the weather this weekend, as we've no kitchen at the moment and we're living off the kindness of others, BBQs and whatever's left in the freezer zapped in the nuclear box!
