Correct me if I'm wrong, but regarding annealing methods for polymers, maintaining temperature in a controllable gradient is more important rather than what medium you do it in. You're just trying to steadily hit the glass transition temperature of the polymer to help the crystalline structure realine, then gradually cooling it back down so it locks into its more aligned form. To my understanding, sand and oil annealing were more of a byproduct of trying to surround the part in a thermal mass that could distribute heat more evenly when early 3D printing enthusiasts were experimenting with kitchen ovens. One benefit I have read in the past about sand however, is it can support the part more evenly reducing uneven sagging or drooping, though I personally haven't tried sand myself.
To put it simply, for most polymers, open-air annealing shouldn't be much different in a well-controlled heat source than sand or oil annealing.
In your case, if you are experiencing melting at the supports, you're already exceeding the glass transition point of the material. I'm assuming you're using an oven?
I don't personally like ovens for annealing but have done a lot of experiments with it in the past. Some tips that could help:
Putting parts dead center of the oven on an elevated rack: Most ovens have a heating element on top and on the bottom. This creates a temperature gradient, where it's hottest closest to the coils. Elevating the part in the oven toward the center as much as possible helps it to hit the more even peak of the gradient from both the top and bottom.
Set the temp lower: The Oven displays incorrect temperatures from the true ambient temp, because it's only reading off of one thermistor, I usually would set the temp a bit lower than what I wanted, and it usually hit closer to the temperature range I wanted.
Measure the part surface temp directly: Use a little multimeter thermistor, or even an IR thermometer and probe or scan the surface of the part directly.
Aim for the minimum glass transition temperature: With oven annealing, I had the most success with hitting the minimum glass transition temperature rather than risking closer towards the melting point.
