Doors – Tilt and turn door brushes against the reveal

Your idea is possible. It will take as you may know already, a custom metal fabricator who is certified, to build to insure all welds will hold up under the weight of the assembly, since it will weigh hundreds of pounds. Using aluminum to make the base, sealed bearings in proper housings for the pivots. Counterbalance filled with lead to ease its operation, and solution to help lower the door in place to keep it from slamming down, like a gas filled piston and rod, like a shock absorber. an aluminum mesh, spot welded in many places to give a way for the tile to bond to the plate that makes the face of the door, with a perimeter angle to dress up the edge so you do not see all the layers at the edge of the door. With all this done, it will need to be powder coated to keep the contact with cement based products separated, so it will not corrode. Your biggest problem will be with your counter balance. When the door raises, it will drop in front of the door. It may be better to use springs or electric lift mechanism, or hydraulics. I made a small sketch to see how it acts together with a counterbalance.

This is by no means a complete sketch, it is missing reinforcements, the hinge pivot is off,etc. Just a picture study on feasibility.

In my opinion a lift system like that is on the rear gates of SUV's is a good way to go, although, should one of them fail....

If the hinges are on the same vertical line, then (as noted by @DA01) the hinge should stay wherever you leave it (absent wind, etc). If the hinges aren't vertically aligned, then the gate will want to swing towards a specific point. You can use this to solve your problem.

Imagine that the gate is swinging on a rod, and can go 360° around the rod. If the rod is vertical then you can put the gate anywhere you want and it will stay. However, if the rod is leaning towards a certain direction, then the gate will tend to swing until it is pointing in that direction (because the gate will be lower at that point).

What if you move the gate to the exact other side of the rod from where it wants to go? It will sit there, balanced. If you then move it in either direction it will continue to swing in that direction until it reaches its low point.

So, what you want to do with your gate is to align the hinges so that the hinge line leans away from the the middle of the gate's range (at 45°). That way the gate will tend to swing away from the 45° point, towards the nearer of 0° and 90°.

Edit: When you do this, you may have to readjust the position of the gate on its hinges in order to have the gate properly fit into its opening. But, once you adjust the post side of the hinges to get the right swing, changes to the gate side of the hinges won't affect the swing, so you won't have to readjust anything.