This page should generate most nearly-regripless twist algs for a given 2-twist or 3-twist corner case that are made from concatenating two 3-style cases, with setups no longer than the provided search depth in axial turn metric (maximum 2 if specifying 2 corners, maximum 3 if specifying 3 corners; these may take a couple of minutes). You can select if you only want regripless algs.
For each alg, the length is displayed (counting, for example, U D as a single move, R2 as two moves, U2 D' as two moves), and the algs are roughly sorted from best to worst. There is a * before the alg if one of the setups has a regrip. Ideas for improving the sorting are welcome.
Type in the location of the U or D sticker on the twisted pieces. For a 2-twist, either leave the third spot blank or type in another solved corner (starting with U or D) to only search for comms involving that corner.