The problem here is that oxygen is displaced by heavier gases, N2 and CO2 being the classic ones. So a region of heightened oxygen is unlikely to form in the first place since the rest of the atmosphere will be constantly displacing the O2 from the area of production. To create enough oxygen fast enough to have the effect you describe would require vast outputs of O2 which you won't get from a natural forest, think more along the lines of the terraforming stations from Aliens pumping out megatonnes of cold O2 that dissipates across the landscape and only mixes with the native atmosphere as it warms up. That would give you the geographically limited high O2 you want but sorry not with a forest, the rate of mixing would be too great.

The problem here is that oxygen is displaced by heavier gases, ${N_2}$ and ${CO_2}$ being the classic ones. So a region of heightened oxygen is unlikely to form in the first place since the rest of the atmosphere will be constantly displacing the ${O_2}$ from the area of production. 

To create enough oxygen fast enough to have the effect you describe would require vast outputs of ${O_2}$ which you won't get from a natural forest, think more along the lines of the terraforming stations from Aliens pumping out megatonnes of cold ${O_2}$ that dissipates across the landscape and only mixes with the native atmosphere as it warms up. That would give you the geographically limited high ${O_2}$ you want but sorry not with a forest, the rate of mixing would be too great.