This is a half-north side, half-east side one, but I think it still fits
I think a route between Hamilton and Cannon Hill could be quite useful, as all of the connections north of the gateway go northwards
Inbound of Hamilton, I’m not sure what path it could take exactly. It could do a turnaround at Hamilton, similar to 304, or a turnaround at Doomben Station, similar to what the 303 does, or head to Nudgee Road towards Toombul, or do what’s suggested with the map and head to RBWH (though this would parallel quite a few routes)
