| I also don't see how fiber reinforcing the "pillars" helps much for bending strength.

I don't know what you mean by 'bending strength'.

| That should only increase the tensile/compression properties of the sandwich.

Pretty much agree.

| But if the fibers are sewn at say a 45° angle, then they will form a truss between the skins. And that should really increase the bending strength.

Agree. An angle would add a lot of stiffness to a lot of weird loadings.

But foam core panels need to bend somewhat even in super flat friendly HP designs. I am not sure ultimate rigidity is a win condition. I return to the hexel sheet's suggestion that the skins carry loads, and the cores just keep them apart. So, to my mind, we only need compressive strength in a core, not rigidity. Actually we need flexibility.

| Will the tow "seep" the epoxy through the hole made while sewing? Like a wick? Or is it the opposite, that the hole is needed to suck epoxy into the hole and soak the tow

Having never done any of this yet, let me tell you how it works... lol
It is my understanding one drills ~2mm holes through the sheets every 40-50 mm for the resin to flow to the back side of the infusion. As well there are 2mm x 2mm channels carved in the foam surface on both sides to ensure the epoxy flows well to and from said through holes.

Weaving/sewing tow in these through holes is, I think, the idea. As it is cheap and easy, and fun experiment.
One imagines any tow should reduce resin flow, but perhaps single lines not enough to matter. Certainly one could pack in too much tow, right?

I think epoxy will flow along tow to some extent. I think the desired flow rate and pressure needed for the resin flow in an infusion is too much to allow a simple stitching through virgin foam to replace drilled holes.

Any prior mention of sewing by me was meant to suggest through the typical drilled holes.