Access R2 over HTTP/3?

Is it possible to access R2 object storage (PUTs and GETs) over HTTP/3?
I currently have a service running in an environment with UDP connectivity but no TCP. This works well with Cloudflare Tunnel since that can connect over QUIC, but I also need object storage.

Currently it uses Google Cloud Storage (since that is accessible over HTTP/3 and thus via QUIC over UDP), but since I’m already using Cloudflare for serving HTTP through the Tunnel, it would be nice if I could switch to R2.

The buckets are not be public and thus I don’t believe it’d be possible to use r2.dev or a custom domain that’s proxied through Cloudflare’s regular web servers (which I do believe would support HTTP/3).

I’m also currently using predesigned URLs (to support things like write-only, no overwrite permissions), in case that factors in.

The only other idea I’ve had so far was to set up a Cloudflare Worker, but I would really prefer not to add another service into the mix. Is it possible to access R2 through my preexisting Cloudflare Tunnel ? Can private buckets be accessed through Cloudflare’s regular, HTTP/3-supporting proxies? Does R2 already support HTTP/3 (or QUIC) and I’m just using it wrong?