In my opinion but only my own observation the Cemetery park could hold the key and may not have been searched thoroughly enough.
I know from Search and Rescue/Recovery call-outs that areas are not searched without some tangible evidence that the missing person is likely to be found in that area. This could be based on a number of factors, e,g.:
1. Previously known to have a connection/frequently visited, e.g. family/friend buried, childhood play area, favourite place, found there before when missing etc
2. Reliable witness evidence or CCTV indicates last known to be in the immediate area
3. Mobile phone ping (GPS or cell site)/last active phone connection in the immediate area
3. Discarded property/vehicle belonging to missing person found at or close to the area
If a need to search such an area is identified then police may bring in voluntary Lowland or Mountain Rescue teams, who have the skills, methodology and experience to do so effectively. They can also provide skilled water rescue technicians who can search areas of water, not precluding the need for a police dive team, as well as steep ground and rope rescue/access teams, search dogs and drones.
The focus of the search in an open/wooded area will be from the last known point and radiating out in concentric circles, using various search methods, but with expert reference to the significant data on lost person behaviour, relevant to different missing person demographics/circumstances of disappearance.
My key point is that it is just not effective to go off on a 'fishing trip' based on individual gut feel. Why is the cemetery any more likely to hold the solution than all the derelict areas, canals, abandoned buildings, building sites, the list is endless?
Operational decisions must be based on information received to enable the best use of resources. Always allow the evidence to lead the way. I suspect the police have more than they have revealed.
