Thanks a lot for the pointers, 3imaj. It led to some interesting reading in a field I wasn't familiar with. These emitters are completely non-isotropic. Their half-angle intensity (FWHM) is only 10 degrees.
The frequency is 890nm, and it's a 5mm LED, not an SMT, so I can't see getting any better than ~5mm from center to center which is ~5 lambda. In all likelihood, they'd be spaced at least one LED width apart to ease manufacturing constraints, so they'd be in far-field territory from one another already.
Thanks too to Hero, I'm already using a low duty cycle / relatively high-current design. This may well belong to another thread in the electronics forum, but my biggest problem so far is, as I ramp the current up, the turn-off time suffers. It takes 10 times longer to turn off than when turning on and I get pretty ugly ringing as it does so. I'm using a BJT for the drive transistor. Does this sound like a saturation problem? Would putting a schottky from base to collector prevent full saturation?