For the next generation of high-performance actuators in the manufacturing industry, High-Temperature Superconductors (HTS) are in consideration to replace the state-of-the-art permanent magnet linear motors. In general, linear motion systems in the manufacturing industry require motion profiles with high acceleration and short repetition times. A consequence is the highly dynamic armature field inducing significant magnetization losses in superconductors and eddy-current losses in the conductive media of a cryostat (cryostat wall, radiation shield and cooling platform). These losses impose significant challenges on the magnitude of cooling power as well as on the thermal stability of superconducting magnets for continuous dynamic performance. Through this work, numerous methods are investigated to reduce AC loss in the cryogenic assembly. These include a choice between a conduction-cooled and bath-cooled solution, affecting eddy-current losses, force density and magnetization loss in superconductors; designs of a cooling platform with slit-patterns to minimize eddy-current losses while not adversely affecting thermal conductance; superconducting coil wound with partially striated turns to reduce loss density at hotspots in a coil; and incorporating flux diverters and magnetic shields for loss reduction. To compare these methods, combinations of semi-analytical modeling and Finite-Element-Analysis (FEA) with an electro-thermal framework is applied to a linear motor composed of DC operated HTS coils in a stator and three-phase AC coils in the mover.