Make sure you (or someone who will use the box) is there when they set it. If someone doesn't know that whoever is using it has to be in front of the box with drawers fully open will likely error on the side of passageway space, and make it unworkable.
Are you planning on a separate workbench or using the top of the box as one? Your builder is worried about the height of the box, but he has to remember that unless someone is planning on rebuilding a starter in the galley while they're cooking, you'll need work space below decks along with your tools.
There's also an ergonomic angle - the boxes are designed to be a certain height with casters - it's even normal to use the space below the box created by the casters as storage - if the box is too short, and you're using the top of the box as a workbench, it'll be a pain (literally) to work on top of.
I'm sure you've thought of this, but I had a friend who converted a 65' tug into a liveaboard, and when he got to your point he didn't take these factors into account.
One final note - in salt air, rust never sleeps. Finding a way to keep your tool area dehumidified and the air clean will go a LONG way toward keeping from having to replace your toolbox (and tools) in 5 or 10 years...