For someone 6'2" tall I would suggest that you want 6'3" headroom or more throughout any areas of the boat where you would normally be standing. You can get by with stooping much of the time on a boat that you only spend weekends and the occasional longer cruise, but on a liveaboard that is going to get old REALLY fast! You don't need that above a berth, or even the "sitting area" of a head, but elsewhere...
You are going to find extremely few boats under 30' with that kind of headroom. In the 30-32 range you'll find more, but they will still probably be the minority. Get up to 34' and above and you'll find plenty of boats with the headroom you need. I am only 6' myself, but if I were looking for a liveaboard I would be focusing on boats in the 34-40 foot range. If I discovered a particular make and model that was shorter, that had the headroom and layout I wanted, I would add that to the list. But I would not spend a lot of time examining shorter boats.
Edited to add: Remember that when a manufacturer quotes a particular amount of headroom on a boat that is often the maximum headroom, and may only occur in one particular spot (usually in the saloon). Again, for living aboard I would not want a boat that has only ONE PLACE where I can stand fully upright. I want that headroom throughout most of the boat.
Thank you, thank you,
thankyou .... I thought I was the only one left who used the correct term i.e. " saloon " .