The problem seems solved, here are the steps I've taken:
added the Pi-Hole's own IP in the static IP list on the pi-hole
chose the exact same IP range on the pi-hole as on the router
After doing these two things, both the router AND the Pi-Hole had DHCP enabled in parallel (which I understand is a no-no, yet still...) and some of the traffic used the Pi-Hole, which gave me some confidence.
Then an hour ago or so, I disabled DHCP on the router and so far so good.