With the focus on the drawing, you can use the Shift transform for that. In the Shift X and the Shift Y boxes first change them to using an Expression, and then for the expression use some random number expression.
For example, (taken from the end of the Computed Fields topic) the expression:
(TABLE CALL ValueSequenceRandomInt(1, 100, [mfd_id])) + 10
Will generate a random number from 10 to 109. Using the same expression for both Shift X and Shift Y will shift the overlapping points a random distance in that range along a diagonal line (since both the X and Y shifts are the same).
If you wanted to spread the points out a bit, but still towards the upper right quadrant, you could use the above expression for Shift X and a different expression for Shift Y, such as...
(TABLE CALL ValueSequenceRandomInt(1, 100, (TABLE CALL ValueSequenceRandomInt(1, 10, [mfd_id]))))
Which generates a random number from 0 to 9 to use as a seed for the outer random function. Make sure your drawing is in a meter or foot based project, not lat/lon, since you want to shift points by dozens of meters, not degrees.