We present the detailed timing and spectral results obtained during the Swift observations of the TeV-detected blazar 1ES 1959+650 in 2016 August-2017 November. The source continued its trend of gradually enhancing X-ray flaring activity in the 0.3-10 keV energy range, starting in 2015 August, and a new highest historical brightness state was recorded twice. A long-term high state was superimposed by both weak and strong flares, and we detected 32 instances of intraday X-ray flux variability, including several occasions of extremely fast fluctuations with fractional amplitudes of 5.4%-7.5% within 1 ks exposures. The 0.3-10 keV spectra generally showed a best fit with the log-parabolic model, yielding a very wide range of the curvature parameter b and the photon index at 1 keV. The position of the synchrotron SED peak Ep showed an extreme variability on various timescales between energies less than 0.1 keV and 7.7 0.7 keV, with 25% of the spectra peaking at hard X-rays. In 2017 May-November, the source mostly showed lower spectral curvature and an anticorrelation b-Ep, expected in the case of efficient stochastic acceleration of X-ray-emitting electrons. The 0.3-100 GeV and optical-UV fluxes also attained their highest historical values in this period, although the latter showed an anticorrelation with the 0.3-10 keV emission, which is explained by the stochastic acceleration of electrons with a narrow initial energy distribution, having an average energy significantly higher than the equilibrium energy.