Trakhak

You say you partly inflate the tube to make sure that it doesn't fold when you insert it in the tire, and then fully deflate the tube.

I think that that last step is the problem.

I also always partly (minimally) inflate the tube and insert it into the tire. But, instead of immediately deflating the tube once it's in the tire, I leave the tube partly inflated and push the tire over the lip of the rim, all the way around one side of the wheel. Or if the tire is too tight on my first attempt, I let a tiny bit of air out of the tube and try again.

Once I have one side of the tire installed in the rim, I check to make sure that the stem is straight. If it isn't, I let a tiny bit of air out and pull the installed side of the tire along the rim until the stem straightens. If it seems appropriate to do so, I might reinflate the tube a bit, to make certain that it doesn't fold.

Finally, I begin seating the tire on the other side of the rim, working it on with both hands symmetrically away from the valve (after having first pushed the valve down into the tire to make sure that the reinforced valve seat doesn't prevent the tire from properly seating at the valve).

It isn't until I get to the point where the tire refuses to be pushed over the rim that I let most (or, if absolutely necessary, all) of the air out of the tube.

Having succeeded in getting both sides of the tire fully into the rim, I then inflate the tire to 10 pounds of pressure or so and check the tire's witness line all the way around the wheel to make sure that the tire is fully and evenly seated.

Once the tire is correctly seated, I inflate to about half of full pressure, check the tire seating again, and then, if the tire looks good, inflate to full pressure.