Magnetars, isolated neutron stars with magnetic-field strengths typically ≳1014 G, exhibit distinctive months-long outburst epochs during which strong evolution of soft X-ray pulse profiles, along with nonthermal magnetospheric emission components, is often observed. Using near-daily NICER observations of the magnetar SGR 1830-0645 during the first 37 days of a recent outburst decay, a pulse peak migration in phase is clearly observed, transforming the pulse shape from an initially triple-peaked to a single-peaked profile. Such peak merging has not been seen before for a magnetar. Our high-resolution phase-resolved spectroscopic analysis reveals no significant evolution of temperature despite the complex initial pulse shape, yet the inferred surface hot spots shrink during peak migration and outburst decay. We suggest two possible origins for this evolution. For internal heating of the surface, tectonic motion of the crust may be its underlying cause. The inferred speed of this crustal motion is ≲100 m day−1, constraining the density of the driving region to ρ ∼ 1010 g cm−3, at a depth of ∼200 m. Alternatively, the hot spots could be heated by particle bombardment from a twisted magnetosphere possessing flux tubes or ropes, somewhat resembling solar coronal loops, that untwist and dissipate on the 30–40 day timescale. The peak migration may then be due to a combination of field-line footpoint motion (necessarily driven by crustal motion) and evolving surface radiation beaming. This novel data set paints a vivid picture of the dynamics associated with magnetar outbursts, yet it also highlights the need for a more generic theoretical picture where magnetosphere and crust are considered in tandem.