Audio Frequency Response Offset in dB
... add whatever Vout is necessary to make the 1kHz point 0dB, then offset all of the Vout values across the measurement range with that same "offset" voltage to obtain the frequency response relative to 1kHz?


You will make the +0.35 dB adjustment by amplifying the signal by +0.35 dB and not by adding an "offset" voltage. This will raise the whole curve by +0.35 dB.


  Initially I just added +0.35dB to the entire curve but after thinking about it, I don't think that makes sense, since it would be changing the output magnitudes at each frequency exponentially.


Not exponentially. "Ratiometrically" would be a better description.

That's what most amplifiers or attenuators are designed to do. Think of a potentiometer in a volume control application, for example. It attenuates by a fixed ratio across the full spectrum (ignoring any parasitic capacitance). 

One of the handy features of using decibels is that we can just add them rather than multiplying ratios and, for audio work, it gives a linear value which is a good approximation to the ears' perceived volume. For example, if we had a -3 dB attenuator followed by a +5 dB amplifier and a -9 dB attenuator we can get the full circuit gain as -3 + 5 -9 = -7 dB.