They're basically light fields, so even though they don't represent any geometry, you could easily integrate them into the rendering pipeline at the path tracing/rasterization stage for Cycles/EEVEE.
I think the "right" way to do it without forking Blender would be to write an OSL shader. Though the way I personally would have done it would be to convert the splat into an angle-dependent Math Node tree for an Emission shader, probably automatically with a Python script.
Trouble is light fields don't block geometry, so they would effectively blend additively and you would see right through them like a hologram. Easy enough to fix though, with a dummy mesh to composite out the background. Or you could just render the splat separately outside Blender, and composite your scene on top of it.
I'm not sure why you would want to, though. The splats couldn't be lit by any of the lights in your scene, nor can they receive shadows cast by any objects in your scene, because they're precomputed light fields. Objects in your scene could be lit by the splats, but it's not immediately clear to me that it would be much more useful or better than just having photos on billboard planes.
I think there might be a misunderstanding that splats provide a way to compute realistic lighting. In reality, they're only a way to store and sample pre-computed or measured lighting AFAIK, hence the need for OP's big camera rig. So integrating them into scene lighting or skeletal animation doesn't really apply.
