Is it possible to phase shift a single harmonic rank without shifting the rest of the distored signal?
Conceptually, what you seem to be proposing seems to be something like passing the entire current of a branch of the grid through a system that extracts specific harmonic currents and injects them back into the grid with a different phase relationship to the fundamental to cancel harmonics originating in another branch. Passing all of the current of a branch through any system would seem to be less efficient than some kind of active or passive filter that would handle only one or several specific harmonics.

A similar concept would be to have the major harmonic generating sources vary their waveform creation strategy in a way that would tend to cancel each other. I found a paper related to that, but I made a mistake in trying to save it. I will try to find it again and post a link later.

Added reference information re above:

Armstrong, Matthew; Atkinson, D.J.; Johnson, C.M.; Abeyasekera, T.D., "Low order harmonic cancellation in a grid connected multiple inverter system via current control parameter randomization," in Power Electronics, IEEE Transactions on , vol.20, no.4, pp.885-892, July 2005
doi: 10.1109/TPEL.2005.850949
Abstract: In grid connected multiple inverter systems, it is normal to synchronize the output current of each inverter to the common network voltage. Any current controller deficiencies, which result in low order harmonics, are also synchronized to the common network voltage. As a result the harmonics produced by individual converters show a high degree of correlation and tend to be additive. Each controller can be tuned to achieve a different harmonic profile so that harmonic cancellation can take place in the overall system, thus reducing the net current total harmonic distortion level. However, inter-inverter communication is required. This paper presents experimental results demonstrating an alternative approach, which is to arrange for the tuning within each inverter to be adjusted automatically with a random component. This results in a harmonic output spectrum that varies with time, but is uncorrelated with the harmonic spectrum of any other inverter in the system. The net harmonics from all the inverters undergo a degree of cancellation and the overall system yields a net improvement in power quality.
Link

Here is a newer article by some of the same authors as the article you linked:

Arghandeh, R.; von Meier, A.; Broadwater, R., "Phasor-based approch for harmonic assesment from multiple distributed energy resources," in PES General Meeting | Conference &amp; Exposition, 2014 IEEE, vol., no., pp.1-5, 27-31 July 2014

Here is an article about measuring harmonics including phase information:

Chakir, M.; Kamwa, I.; Le Huy, H., "Extended C37.118.1 PMU Algorithms for Joint Tracking of Fundamental and Harmonic Phasors in Stressed Power Systems and Microgrids," in Power Delivery, IEEE Transactions on, vol.29, no.3, pp.1465-1480, June 2014