R302.7 Under-Stair Protection – does drywall need to be below stringers or just treads and risers?

I am finishing a room in my basement, and a wall will butt up against where the stairs are. I'm planning on making a small door to access the volume below the stairs for a small storage area.

The building inspector said I needed to put drywall below the stairs for fire protection.

The stairs have a middle string. If I place the drywall over the stringer, that will significantly reduce the available volume.

Can I fulfill this requirement by putting two tightly fitting drywall panels in the spaces between the stringers, leaving the middle stringer exposed?

Text of relevant ICC code:

R302.7 Under-Stair Protection

Enclosed accessible space under stairs shall have walls, under-stair surface and any soffits protected on the enclosed side with 1/2-inch (12.7 mm) gypsum board.

Otherwise, simply "coating" the middle stringer would be a compliant alternative to maximize accessible volume, would it not?

Here are some pictures from under the stairs. The difference between the plane of the bottom of the stringers vs the bottoms of the treads and risers is a significant amount of space to store stuff.