The dynamics of the spin-orbit coupling in elegant and standard Hermite-Gaussian (HG), Laguerre-Gaussian (LG), and Bessel-Gaussian (BG) beams propagating through a uniaxial crystal are analyzed. We consider the structure of the electric fields of the paraxial beams and show that the extreme values of the spin and orbital angular momenta are inherent in the elegant HG and LG of high orders. The spin-orbit coupling in the BG beam of the lowest order can result in nearly 100% energy transport from a vortex-free beam to the vortex-bearing beam at a relatively small crystal length. The extreme spin-orbit coupling does not manifest itself in standard HG and LG beams.