Eugenia are pretty commonly used as bonsai, especially in the north, as under lights "indoor for winter" bonsai. Yours shrubs are great starting points for bonsai as you already have trunks with some caliper.
Best time to dig these is while they are in active growth. I don't know the St Petersburg Florida climate very well, but I suspect somewhere in March or April, when they have started flowering is a good time.
You can all in one day dig, and prune back severely pot up and wire up the new bonsai trees. Key is, wait until they are in active growth, you want to see new branches extending and possibly flowers. If done at this time, you can remove 80% of the roots, and 90% of the foliage and still get good back budding and rapid development of new roots.
If you do the digging and repotting now, October-November=December - while the bushes are entering semi-dormancy, you may not get a vigorous response. In fact there is a chance the bushes won't survive.
I have grown Eugenia as an under lights for winter "indoor bonsai". So my experience is limited to smaller specimens. Contact the good people at Wigert's and ask them when the best time to Dig-Chop-Style landscape Eugenia to make them into bonsai. They are friendly, and in Fort Meyer's area, so they know your climate and how Eugenia responds to your climate. See what Wigert's says, as they sell this species as part of their regular inventory, so they have hands on experience. They also stock bonsai supplies, and have a good selection of bonsai pots.
Before your start the project of digging these up, plan on them in training pots for a couple years before you move them to more expensive bonsai pots. Though, you could go direct to bonsai pots. I like using Anderson flats for the training pot, they are 16 x 16 x 5 inches heavy duty plastic flats with mesh bottoms. This size holds about 3 gallons of potting mix. But you can also make wooden training boxes of similar dimensions. Most "off the shelf" bonsai pots are less than 4 inches deep. If you want to avoid having to have custom bonsai pots made for your tree, it is important to reduce the root mass drastically, to create a shallow but wide root system. Do not use deep containers as your training pots, try to find wide, but shallow containers, and flatten the bottom of the root mass to a depth of less than 5 inches. Be sure to wire the newly collected tree into the training pot. It must be secure an not have any wobble, before you fill in with potting media. If it has wobble, newly developing roots will break if the tree is hit by wind, or jostled by kids, yourself when watering or moving the pot around, or by animals moving through the backyard. Wobbly trees loose roots and die. Wire it in firmly, before finishing the filling of the pot with media.
Key is having several pot options, and sufficient potting media on hand before you start to dig. Don't dig spontaneously, have everything ready, then dig.