I have been hesitant to reply to the question because I have never drilled out pop rivets from that kind of application or location. I have removed a lot of pop rivets from gunwales and hulls including Royalex and composite.
Almost all pop rivets in canoe manufacture or outfitting are 3/16” (5mm) diameter, the most common exception being 1/8” dia pop rivets used on spray skirt snaps
To remove 3/16” dia pop rivets use a 3/16” metal drill, centered in the little dimple of the pop rivet head. Make sure it is aligned with the pop rivet shank, not angled. Drill just the flanged head of the pop rivet and the head will spin off on the drill. That’s a known part.
I am guessing those are standard head rivets, which have a 3/8” flange head. There are wider 5/8” flanged pop rivets, typically used on pop riveted foot braces, but there would be no need for those to seat the aluminum plate, and it doesn’t matter for drilling off the head.
With the heads drilled off you can remove the broken plate and have a look underneath, and that leaves me at the guessing part.
You could try to drill out the remaining rivet shank and reinstall a new support in the same holes (definitely use a stop). But drilling the embedded rivet shank or removing it entirely seems fraught with danger, like inadvertently enlarging the hole so the new pop rivets won’t hold.
I’d tap whatever shank is exposed on the interior back into the foam/kevlar support and plug the hole with a dab of thickened epoxy. Take the replacement plate and drill new off-set holes in it, so the plate can be put back in the same exact position with the new plate holes aimed at virgin areas of the kevlar/foam side support.
Mark and drill one hole (use the stop again) and install that pop rivet. Then drill the second hole with the plate held in situ, so the alignment of plate hole and kev/foam hole is assured to be perfectly aligned.
What length 3/16”/5mm diameter pop rivet? Hard to say from the photos, probably ¼” (6mm) grip range.
