I have a Morgan 30 (1971 vintage) and would have no hesitation in recommending her as an offshore boat. This is a pretty seakindly design with good sailing manners (although the centerboard does need to be fully operational to get the best results, especially when sailing to windward). I have read that the cockpit can be very wet in a big sea but, so far, I haven't experienced that problem.
The main issues for me are the poor draining arrangements in the cockpit and the lack of a bridge deck with the resulting danger of water flooding down the companionway. I intend to fit additional drains next season and I just make sure that at least the lower washboard is in place when things get rough!
As others have commented, the main thing when going offshore is to be confident that all your gear is fully up to snuff.
Leith (rhymes with teeth) is the port of the City of Edinburgh in Scotland. A Leither is someone who comes from that area.
I must go down to the sea again, to the lonely sea and the sky - I left my shoes and socks there, I wonder if they're dry?