ok, i wont be able to accurately test the total capacitance (and real delay), but i can effectively combat that issue by adjusting the trigger threshold on the scope. if it takes 1ms to get a rise to 1v trigger threshold and 1ms is too long, i can turn the trigger threshold down.R changes the sensitivity since a given amount of light impinging on a photo-diode generates a given amount of current. Thus the larger the R, the more voltage drop is generated across that R.
You didn't include any stray capacitance from the layout and the 'scope input.
Even with a 10:1 probe for the 'scope the strays will likely be at least 20-30pF.
at 15x the pF i mentioned earlier (so about 22.5pF) the RC is just 225ns (2t is 450ns) = 0.450μs. i would be concerned if 1RC was close to 10μs as things are happening at the speed of ~12μs.
the DSO gear i have (cheap stuff) will likely have cap in the area of 120pF, which pushes the 1RC up around 1.2μs.
interestingly enough, the light beam approach seems easy from the electronics side, but very hard from the physical alignment side, of which seems to be a difficult challenge.If you don't want to put anything near the path of the bullet then maybe a sound or vibration sensor would work. I have seen this done in shooting simulators.