As per the Process for reviewing classic confinement snaps, unfortunately the inability to get a snap working under strict confinement is not a sufficient precondition to be granted the use of classic confinement.
Not every application is able to be packaged as a strictly confined snap, and for those that are not, they must have a requirement for classic confinement as per that page - but again, this snap doesn’t seem to need to execute arbitrary binaries from the host or access things outside the snap’s runtime etc. Instead it would seem to need an interface that provides direct access to underlying disk devices. This does not currently exist but perhaps the block-devices interface which provides partition level access may be sufficient?
Also for /proc/$id/mounts you could try using mount-observe.
Thanks