Base Hammer Production
With all of that being said, my justification for NOT settling in place is that I don't like the long-term viability of that spot since it lacks hammers for the capital.
Let's fairly assume that settling-in-place will not get to keep all 4 Food Resources... either a City to the east or the west will likely borrow at least one of these Food Resources, perhaps two of them... but 2 Food Resources will be more than sufficient to work all of the production-based squares for either settling in-place or settling on the PHFor.
So, I'm going to ignore Food-based production and just look at Hammer-based production here.
Settle-in-place:
City Centre = 1 Hammer
east-north-eastern PHFor that gets Mined = 4 Hammers
western GH that gets Mined = 3 Hammers
Total = 8 Hammers
Settle on the PH:
City Centre = 2 Hammers
northern GH that gets Mined = 3 Hammers
south-eastern GH that gets Mined = 3 Hammers
Total = 8 Hammers
So, I'm a bit lost how settling in-place differs from settling on the PH in terms of Hammer output. Ignoring whipping-based production and after our Worker has improved the relevant Hills squares (for a capital, this situation will apply for the majority of the game), the production output appears to be identical.
Forest Chopping
In fact, I could argue that by settling-in-place, I'd be more heavily leaning towards keeping the 2 GFor squares, for +1 Health (which equates to more Food which translates into additional production) or for occasionally working those 2 squares for a bit of extra production, say, if we want to build a Wonder.
By settling on the PHFor, you already "eat up" one Forest, and with only 1 Forest remaining the big fat cross, you "might as well" chop the remaining Forest... which actually equates to an equal amount of Hammer production from Forest Chops as settling-in-place if settling-in-place saves its two GFor squares.
If by settling-in-place we start clear-cutting, we actually get more Forest-Chop-production than by settling on the PHFor. So, once again, I fail to see how settling on the PHFor provides more production than by settling in-place.
Convince Me
Note that I am not necessarily pushing for any settling location yet... I still have yet to be convinced of a superior choice... which is why I asked people to try and articulate their reasoning, to better convince me of their reasoning and to help me with my voting.