Personally I'd take this with the addition of having some kind of a safety net that would auto-grant a request in case of a House Gov's inactivity. Maybe even just staff approving it on their behalf.
Since we actually had this reveal on the Bristol Discord, I think an easier solution is to make public who sits in what Gov. It's to 99.99% the OFs 1ics but making this bit public so people can do step 1 of reaching out on Discord would already do wonders since you yourself had no clue who to reach out to. And perhaps the Gov running lads do the same vice versa when really busy (rip me here for our instance, I know) A safety net feels appropriate post 14 days but if that's the case frequently, should they actually run the Gov then?