Could you run some kind of hybrid DHT where part of it was Webrtc and part was plain HTTP(S) / WebSocket?

There are some nodes (desktop clients with UPNP, dedicated servers) that can accept browser connections. Those nodes could then help you exchange offers/answers to give you connections with the Webrtc-only ones, and those could facilitate offer/answer exchanges with their peers in turn.

It'd be dog-slow compared to the single-udp-packet-in, single-udp-packet-out philosophy of traditional mainline DHT, but I don't see why the idea couldn't work in principle.

I think a much bigger problem is content discovery and update distribution. You can't really do decentralized search because it'd very quickly get sybil-attacked to death. You'd always need some kind of centralized, trusted content index, but not necessarily one hosted on a centralized server. If you could have a reliable way to go from a pubkey to the latest hash signed by that pubkey in a decentralized way, + E.G. a Sqlite extension to get pages on-demand via WebTorrent, that would get you a long way towards solving the problem.