If you want to identify the problem, you should reduce your existing code, not rewrite it. If there is an error, it will either remain in the reduced code or you will know which piece of code you just removed when it started working as expected.

Alright let me rephrase my previous statement then,

I wrote the part that does just the basic proj and model setup, again (i copied my existing code), into a smaller program.

The problem disappeared. (It behaved as one would expect.)

I found that you swapped the b and t values of glOrtho and found that I had culling set the wrong way (which added to the mystery of obscured objects being drawn).

I've fixed the issue in the bigger project.