I do not know how you could detect the increase in the velocity of a photon. I do think that the observed 'Gravitational lensing' is caused by the iherent 'force' within the area of lower spacetime density.
The mass that we are so familiar with creates a lower spacetime density within itself when compared to the familiar 'outer space'. This effect is due to the fact that there is more 'activity' or 'energy' or 'motion' with in the mass than there is in outer space. In outer space the fundamental 'kinetic force' accelerates to the final velocity of Einstein's 'C'. Where as, in the molecular mass the acceleration is the 'C' plus all the other thermal and 'mechanical' activity. Simply substitute fundamental values to Bernoulli's principle to get mathematical confirmation of the effects. Use Einstein's 'C' for the constant.