There are a number of things here.
1/ You have some control over where the base of the supports are placed. By placing the touchpoints on the sides of the model, rather than just the bottom, Preform will throw bases outwards, making a wider support base.
2/ I would be tempted to add two or three touchpoints up the edge of model to bind the support structure to the model, it will also help widen the support bases. You could also think about building this piece directly on the build platform.
3/ Green resin absorbs IPA, and especially DPM/TPM, so if the piece is in the wash too long finer sections, like supports will distort more than the main body of the piece.