Since we know the position of the source of the photon, we can determine its trajectory from the source to the detector, once we know its final position on the detector.
Photons don't have trajectories. It's perfectly possible to consider a situation where you know the starting point of the photon to a high accuracy (say, you know it was produced at a molecule which is tightly bound at a specific location) and that you know the position at which it was detected (you know which pixel clicked), but that knowledge does not tell you anything about what happened between those two times. If you are not actively performing a projective measurement on position (resp. 400
momentum) at a given time $t$, then QM is explicitly restrained from saying anything about that position (resp. momentum) at that time.
I see nothing that would prevent, as a practical matter, such a detector from also giving us the energy of the photon to arbitrary precision, subject only to practical, technological constraints.
Since the speed of light is always $c$, and the formula for the momentum of a photon is simply $h/\lambda$, it follows that we can calculate the position, and momentum of the photon, without any apparent constraints that relate these two values.
It's perfectly reasonable to add a spectrometer behind your detector pixel so that you also do a projective measurement on frequency, and this does give you a definite value for the photon momentum.
However, that procedure doesn't tell you anything about the direction in which that photon is headed, so you don't have any real knowledge of the photon momentum, which is a vector quantity.
Moreover, the fact that you're post-selecting on the photon frequency means that the initial pretense that the photon frequency was undetermined can be stripped away in this context, and your configuration is equivalent to one in which you knew perfectly well (say, because of the way you've tuned your molecule's emission lines) what the photon frequency was. In that picture, you have a molecule emitting a narrow-band single-photon wavepacket, which immediately proceeds to fill up all of the available space in whatever Helmholtz mode is driven by the transition, evolving into a complicated spatial wavefunction with a large spatial and momentum support, which covers a large fraction of your detector, after which one of the detector pixels clicks.
And once you frame things like that, it should be clearer that the information offered by that detector click is rather limited, since the next time you re-run the experiment you'll get a click from a different pixel. 795