Time uncertainty of an ADC sample for a given sampling frequency
Right now, I am working under the assumption that sample at fs results in a timing uncertainty of 1/fs.

This is not correct unless you are undersampling.  Timing uncertainty in a Nyquist sampled signal is determined by SNR, not sampling rate since (per the Sampling Theorem) you have recorded the signal exactly and can reconstruct it with as small of a time step as you like.  Thus what really limits you is noise in the measurement, not the sampling rate of the recording.
In general, you should expect to do much, much better than 1/fs.