Great job, Joe! Before I answer your questions, I just wanted to let you know that your photos are showing up on my end.
For good or ill, everything starts out in the roots. The first thing I noticed when I looked at the photos of your new cacti in your "New plants/ newbie questions" thread -- the seller's mix contains too much soil and organic materials (probably tree bark). Fine for jungle cacti like Hatiora, Schlumbergera, etc., but not for desert cacti. Holes anywhere on the plant are a cause for concern, and holes below the soil line are especially concerning because that's where roots should be. My educated guess is that roots in the overly-rich mix rotted away, leaving the hole you see in the base. Also, I don't like this...
The best thing you could've done is exactly what you did, and your thorough cleaning job revealed these trouble spots you wouldn't have seen otherwise. Before you even think about repotting, let the hole and the exposed areas indicated in the circles dry and form a callus. My sense of caution leads me recommending that you give it a month, then I think it'll be safe for you to repot. Two weeks after the repot, give the "problem children" some light watering -- sip, don't soak yet. Do the same a week or two after that. Gradually increase the amount of water with each watering -- what this does is tease new roots into growing as they seek out water. At some point, the plants' root systems should be grown in well enough for deep watering. There's no hard-and-fast rule for knowing how long it'll take going from sips to soaks, so you'll just need to use some judgment. You had to contend with the ill, but if you come up with the right mix, you'll enjoy the good as healthier roots produce healthier cacti. By the way, you should keep them in the shade while they're in their bare-root state, then gradually acclimate them to full sun after they're repotted.
The buds on your plants may or may not go into bloom (I think the big bud on one might be far enough along to flower). Believe it or not, even desert cacti go through a form of "transplant shock", so don't be surprised if the buds dry up.
Questions -- are you fertilizing your cacti? If so, what fertilizer are you using? Let me know about the brand name, and what the NPK numbers are on the label.
If you just want photos without all the blather, please visit my Flickr gallery
My location: Los Angeles, CA (Zone 10b)