try to use transient with PWL at the input changing very slowly. For ex. start from 1V and go to 1.4 in 1 us and after go back to 1 in another us. The result will be very close to DC (the slower the input changes the better you accuracy).

If your curcuit (comparator???) is clocked define the accuracy by changing input signal during 1 clock cycle. (for ex. if you want 1 mV accuracy, make the input changing 1 mV during 1 clock cycle).

I not sure but I think the parameteric DC sweep uses the solution at the last parameter value in the sweep as the initial guess for the solution at the next sweep value. If that is indeed true, you could see hytsteresis from a DC sweep... if you could do the reverse direction. If you really want to use the DC sweep, you could try introducing an intermediate variable, say x, and set x equal to a periodic function of the actual sweep parameter. For example, suppose you want to sweep a voltage from -1 to 1 volts and then back to -1 volts. Define x(y)=-cos(y) in your ADE window and then sweep y from 0 to 2pi.