Probably any root pruning should be done just before they begin their growth .. so that would be around April. If you're just potting up to the next size, and the plant is rootbound, I do not think it hurts to repot in the early summer. I do all my repotting outside, usually in June. I just don't have the room to do it indoors when the weather is cold (and I'm too much of a wimp to do it outside when it's cold!). By June the plants are really getting going and are putting out a lot of new roots. As long as I don't damage the root system too much, they don't skip a beat.

I'd wait until they start really growing before repotting. Usually by early June they should get going. Then the chance of overwatering (or getting too much rainfall) is much less. However, if you are keeping them in a greenhouse or very warm and bright place, and if they are currently in growth, you could probably repot any time. Once they pick up speed in their growth, I'd move them up to a pot at least a foot in diameter.

Take all of this with a grain of salt as I've only been raising plumerias for a little over a year. Agree with wsb-man about getting some help training that curve. Know someone here who is an expert in this kind of thing and he'll be chiming in soon, just know it :) As far as repotting- you would of course be stressing the plant, and I'd give some chances that the inflos might not survive. But the soil you have it in is obviously poor with sad drainage. I'd risk losing the inflos for getting the plant in some healthy soil. Everyone uses something different for soil, but the standard is 5:1:1. That's 5 parts pine bark fines, 1 part perlite, 1 part potting mix like Miracle Grow (not the Moisture Control). If I don't have pine bark fines I use Reptibark on Amazon, it's expensive but a good investment. (Your pot looks like the big bag would prob be best). Be sure your pot has good drainage...several good size drainage holes. What are you fertilizing with? Best wishes. Nancy

I wouldn't plant it deeper as that's just going to induce rot in the buried leaf axils, but you could stake it if you'd like. Or you could get a taller planter and still plant the aloe at the same depth into the soil but have more empty space up top and use the taller sides to help prop it up/control it, if that makes sense. I'd probably also amend the soil to be more gritty/well draining if it's not already of that ilk (it looks a bit too brown for my liking; I like a healthy amount of perlite and lava rock mixed in).