Doors – Minimum unfinished basement door height

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....

With steel sheetmetal studs fastened to sheetrock or plywood, the wall is plenty strong enough to securely support 200+ pounds—provided the load is attached and distributed properly. Either one alone (plywood or studs) can hold that weight, but in combination they are much stronger than the sum of their capacities.

Note that the floor will carry most of the load with the framing conducting the load downward depending mostly on the non-compressible aspect of the materials. If you are skeptical, visit a metal stud store, place one of the studs upright on the floor and stress it by pushing downward into the floor. The only way you can cause deformation is with a very large force (800+ pounds) or flexing it laterally.

I looked for specifications, but they are surprisingly difficult to apply to this use. If there is any doubt, you can always reduce the stud spacing to like 8 or 12 inches—They aren't so expensive that it would discourage a little overkill.