Getting overly complicated logic functions when designing a state machine, is there any way to simplify them?
you can simplify the resulting number of logic gates visually (not by using formulas)

just reformat the equations and you will see patterns

q1+ = (q0)(q1)(x0)  + (q0)(x1)(x0') + (q1)(x0)(x1)

q0+ = (q0)(q1)      +                 (q1)(x0)(x1)  + (q0')(q1')(x0')(x1')

u   = (q0)(q1)(x0)  + (q0)(x1)(q1)  + (q1)(x0)(x1)