How does one calculate the spectral irradiance from an array of IR LEDs?
Let me give you some perhaps useless or useful background info, but you are on the right track.  I presume you chose this design using 40 wide-angle LEDs to increase the intensity over a very wide area much bigger than the head when at this range you could have used fewer brighter 5mm LEDs to achieve the same intensity at low current or much more intensity and still be under the safety limit.

The steradian is a useful term for computing the flux at a distance to normalize the radiant power into a standard lens cone angle regardless of the lens used or not. When no lens is used, ie. a flat emitter, the beam pattern is said to be a Lambertian response of 160 deg which is defined by the -3dB point or half power.
The plane aperture angle of 2θ ≈ 1.144 rad or 65.54° for 1 steradian which is smaller than your IR LED.  Thus the 35 mW of IR power is reduced to 11 mW/sr.
The total beam width for optical LEDs are given as 2θ while IR LED's often narrow beam in a 5mm Lens are much brighter but if it was 6 deg, it could be off centre by as much as 1 deg so they centre the peak power and specify the half-angle, θ instead.