The timing would be late fall or spring just prior to buds opening, however cutting back below any branching at all doesn't work on every tree, especially one that might have been grafted (as most nursery bought prunus are now). Can you try an airlayer in the spring?

There was a fantastic article in an old issue of International Bonsai about developing mume. In this illustrated article, all the trees were started as cuttings, and each fall they were dug and root pruned, and heeled in in a sand bed (for those with mild winters). Just don't let them freeze too hard. The timing was, in spring they are replanted in the ground, because they can get triple the trunk growth that they get in a pot of any size. The branches grow as long as you can let them, then cut them back in the fall, dig up and prune the roots. Remove all upward and downward growing vertical roots and heel them in for the winter. Your first big prune will be the first fall, and you will cut the growth about 2/3 the final height you want the tree. Use the pruning bits for new cuttings. Cut straight across, not at an angle. Second fall, you will cut one of the top vertical branches as your new trunk line about 1/2 to 3/4 inches higher than the first cut. The distance can vary depending on what look you want. This measure is for massive taper. All the other branches will be long, cut them off also horizontally. Don't worry about whats left, that will be carved when the time is right. Each year let the tree grow by feedin heavily, each fall prune back hard and do your root work to promote a spreading nebari.

When you get the trunk to the size and taper you want, then you will begin making branches, and not before. What is true of all bonsai is especially true of prunus mume: you can work on the trunk or the branches, but not both at the same time. Working on branches and keeping them in proportion requires that the tree be grown in a pot. They get too big and can't be wired properly in the ground.

Please forgive me, I am quoting from memory, but I did reread this article yesterday.

Here is a link that might be useful: Sashi-eda Bonsai

Chris,
Thanks for taking the time to provide a detailed response to my inquiry. You state that the first big "prune" will take place the first fall cutting the tree to about 2/3 of the height for the final product. Would you clarify this? Pruning as you describe it seems to involve removing laterals but not the main trunk. The lowest laterals on my tree are higher up than what I want the final product to be and thus, I am thinking of a chop that would remove the entire crown. Another person has recommended that a chop be done after the new leaves have had a chance to harden, in June or early July. That should give the trunk a chance to resprout.

(After taking dormant cuttings in winter and burying them in bundles in wet sand, lift them in spring and look for callus formation. Callus is good. Put them in the ground for the year. In your case you can lift they rooted cuttings in fall and heel them in in another bed, but it's certainly not required.)

Quoting from International Bonsai Magazine, 1982, NO.1, P5, Tomigoro Komaki:
"The plants are dug in early spring, prior to growth, and trimmed. Heavy roots and smaller ones appearing above the root system are eliminated. The large heavy roots are cut back to about one-half inch. It is important that all roots are trimmed to this lenth. Roots developing downwards from the trunk and others growing downward from the radiating roots are also trimmed to allow the plant to sit flat.
The trunk is cut back to about one inch above the root system, retaining two buds. The cut is made on and angle with the upper bud on the outside. The wound will be large, but this is not important at this stage of development." (Emphasis added).

For the next few years you will remove all the branches by cutting horizontally. Don't carve the wounds until later.

Please realize that I am quoting from another author's work, and I have never developed prunus mume using this or any other method. However, it's a good, scholarly article that I believe shows an excellent way to produce massive taper on mume in a short amount of time.