We extend profile domain pulsar timing to incorporate wide-band effects such as frequencydependent profile evolution and broad-band shape variation in the pulse profile. We also incorporate models for temporal variations in both pulse width and in the separation in phase of the main pulse and interpulse. We perform the analysis with both nested sampling and Hamiltonian Monte Carlo methods. In the latter case, we introduce a new parametrization of the posterior that is extremely efficient in the low signal-to-noise regime and can be readily applied to a wide range of scientific problems. We apply this methodology to a series of simulations, and to between seven and nine years of observations for PSRs J1713+0747, J1744-1134 and J1909-3744 with frequency coverage that spans 700-3600 Mhz. We use a smooth model for profile evolution across the full frequency range, and compare smooth and piecewise models for the temporal variations in dispersion measure (DM). We find that the profile domain framework consistently results in improved timing precision compared to the standard analysis paradigm by as much as 40 per cent for timing parameters. Incorporating smoothness in the DM variations into the model further improves timing precision by as much as 30 per cent. For PSR J1713+0747, we also detect pulse shape variation uncorrelated between epochs, which we attribute to variation intrinsic to the pulsar at a level consistent with previously published analyses. Not accounting for this shape variation biases the measured arrival times at the level of ~30 ns, the same order of magnitude as the expected shift due to gravitational waves in the pulsar timing band.