Yes, check the figure often when figuring a mirror. Often 5 strokes or so can bring a 1/8 wave mirror to that 1/20th or better figure.
The big thing when figuring is that you need to cover the entire zone with your work, not just some few parts of it so turn the work with each and every stroke!
As to polishing, use the short strokes of 1/3 of the mirror's dia. for the length of the stroke and don't go fast as the pitch will heat up zones in the mirror and you will have walking zones all over the place. You will also tend to collect a turned up edge when doing it fast.
The polish will start in the center (with the mirror on top) and proceed to the outside quickly. If you are having problems getting the edge of the polish to walk out fairly quickly, turn the mirror to the bottom and work that way. That will cause the edge to polish first and work it's way to the center and if you flip along the way, you will generally have a hole in the center of some thickness which may help with parabolizing as you finish up.