Where does the additional 1 proton cost of oxidative phosphorylation come from?
The energy required for the ATP production by ATP synthase is obtained from movement of ions (H+ or in some cases Na+) downstream of their potential (proton motive force). I guess, there is no exact stoichiometric exchange as in case of ion pumps. The rotation of the motor is generated by the movement of protons through a channel. The H+/ATP ratio is estimated using biophysical/biochemical techniques.

Brand and Lehninger (1977) estimated this ratio to be greater than 3.

Turina et al. (2003) recalculated this ratio using constituted liposomes and their estimate is  3.9 ± 0.2. 

This is an excerpt from a more recent study on chloroplast ATP synthase by Hahn et al (2018).


  The symmetry mismatch between the 14-fold Fo rotor and the
  near-threefold F1 head means that the number of c subunits rotating
  past subunit a to generate one ATP is not an integer. cF1Fo requires,
  on average, 4.67 c subunits, or protons, to produce one ATP. The
  nearest integral numbers of c subunits per step would be 4, 5, and 5,
  equivalent to rotation angles of 103°, 129°, and 129°. Surprisingly
  however, the three conformations are separated by rotations of 103°,
  112°, and 145°, or 4, 4.4, and 5.6 c subunits (fig. S5C). This means
  that the position of the c subunits relative to subunit a in the three
  conformations differs.


The structure and efficiency of chloroplast ATP synthase may be a little different but what I want to emphasize is that there is no exact exchange of protons and ATP.