We have used NSF’s Karl G. Jansky Very Large Array to observe a sample of five known radio-emitting late-L and T dwarfs ranging in age from ~0.2 to 3.4 Gyr. We observed each target for seven hours, extending to higher frequencies than previously attempted and establishing proportionally higher limits on maximum surface magnetic field strengths. Detections of circularly polarized pulses at 8–12 GHz yield measurements of 3.2–4.1 kG localized magnetic fields on four of our targets, including the archetypal cloud variable and likely planetary-mass object T2.5 dwarf SIMP J01365663+0933473. We additionally detect a pulse at 15–16.5 GHz for the T6.5 dwarf 2MASS 10475385+2124234, corresponding to a localized 5.6 kG field strength. For the same object, we tentatively detect a 16.5–18 GHz pulse, corresponding to a localized 6.2 kG field strength. We measure rotation periods between ~1.47–2.28 hr for 2MASS J10430758+2225236, 2MASS J12373919+6526148, and SDSS J04234858–0414035, supporting (i) an emerging consensus that rapid rotation may be important for producing strong dipole fields in convective dynamos, and/or (ii) rapid rotation is a key ingredient for driving the current systems powering auroral radio emission. We observe evidence of variable structure in the frequency-dependent time series of our targets on timescales shorter than a rotation period, suggesting a higher degree of variability in the current systems near the surfaces of brown dwarfs. Finally, we find that age, mass, and temperature together cannot account for the strong magnetic fields produced by our targets.