Just to note something these two ways that the sentence have been rearranged seem strange to me:
（２） 公園で私はお弁当を食べた。
（３） お弁当を私は公園で食べた。
If I could translate it I might read the first one...
As for park by way of me ate lunchbox
The second one...
As for lunch box, I (not sure where to fill in を for this) park by way of eating
Now the original sentence makes a lot more sense and maybe it's just me reading too much into it.
My translations are not perfect because I did them and my Japanese is not great.
Just to note something these
Just to note something these two ways that the sentence have been rearranged seem strange to me:
（２） 公園で私はお弁当を食べた。
（３） お弁当を私は公園で食べた。
If I could translate it I might read the first one...
As for park by way of me ate lunchbox
The second one...
As for lunch box, I (not sure where to fill in を for this) park by way of eating
Now the original sentence makes a lot more sense and maybe it's just me reading too much into it.
My translations are not perfect because I did them and my Japanese is not great.