What are some suitable methods for removing low-frequency line noise from measured data prior to system identification/deconvolution?
Taking a quick look at your acquisition: this doesn't look too terrible in terms of noise, however, the acquisition window looks way too short. With a 60ms window your frequency resolution is only 160 Hz. From the looks of it, you will also get a massive truncation error. As a rough rule of thumb, you want the acquisition window long enough so that the impulse response visually disappears in the noise.  

Specific answers (although they may not help given the truncation error)


If it's really line (like in AC supply voltage hum) noise you can measure the exact location and notch it out for the fundamental and the harmonics.
Sure. Take the mean and subtract. However, again, the window is way too short to get decent low frequency resolution.


A bunch of tips


Make the acquisition window long enough to capture the complete impulse response
Take an acquisition with no excitation. That's your noise floor
Take an acquisition with excitation. That's your signal
Compare signal spectrum to noise floor spectrum. Calculate SNR as a function of frequency
You want at least 10 dB SNR for a decent measurement. Frequencies must either meet that or be so low in level that they don't matter (&lt; at least 20 dB of "the bulk")


If that can't be done there are more esoteric methods like Wiener filtering and/or reconstructive modelling, but it's certainly preferable to clean up the measurement process.