You said the board is 14" long, that's a good 200nH+ end to end. You haven't provided a layout so I have no way to tell if that's a representative figure or not, but I have provided the information above to make that estimation.
What does 200nH resonate with 10uF at?
Zo = sqrt(L/C) = sqrt((0.2uH) / (10uF)) ~= 0.14R
Fo = 1 / (2 pi sqrt(LC)) = 1 / (2 pi sqrt((0.2uH)(10uF))) = 112kHz
Zo works against the ESR of the cap in question (probably the 10uF on the long trace), forming a series resonant tank with Q ~ 14 say. Which in turn means an impedance peak up to about 2 ohms at the capacitor.
Seems like a frequency that wouldn't be very friendly to an LDO, is that your problem -- excessive ripple passing the LDO?
What's the source of ripple anyway, other loads? A "few mA" LDO isn't much of a load, certainly nothing to warrant stacking 40 more uF into a design.
Speaking of big ceramics, those 100uF are probably not 100uF under bias, has that been checked as well? They might not be needed at all if the 2200uF is doing its job. (And is that much really needed? What are the other loads doing?)
This is the study of PDN (power distribution network) analysis, you can draw out the equivalent circuit and simulate it if you like. See what values do well, or lead to strong impedance peaks or poor filtering, etc.
Tim