Graham I wouldn't remove half at one time. Definitely needs to be thinned to allow the wind to go through the canopy without being able to pull the tree over. You will always have light shade with this tree. Which is preferable to heavy shade.
If you could look at these branches coming from the main trunk, the branches to remove will have diameters drastically different to the diameter of the trunk. Your truck is what? Say 10"? The branches that are less than 5" in diameter; 2 or 3" that are redundant meaning there are more than one branch in the same vicinity should be removed from the trunk. You need to see big holes in the canopy. Where are your normal winds coming from?
This is a start. Learning to use this new application.
More pictures I could draw more 'cuts'...the ones I marked might not be all necessary to do...such as all 3 of the cuts on the left. I need to see a bigger picture. But do you see the size of the branches in relation to the size of the trunk? Most all branches will be removed from the trunk. Otherwise you'll promote more growth, density.
This one is tough to see. I hope that this helps you see what needs to go...a little anyway. Doesn't matter the view, what matters is that your canopy is not lopsided and not pruned too quickly. Once you get started you'll see the pattern of what branches need to go and which ones absolutely have to stay.
This last one maybe I need to make the orange 'cuts' thinner. Ugh. More pictures, closeups as well as full views of your tree. Graham, are you planning on doing this work? Got insurance, great medical? Grins...you are working with an arborist? I am better than most at pruning but this is one big tree. I would love to help save it, more pictures. More orange 'cuts'...? Where is your home going to be built in relation to this tree...heck on your site?