I have not much experiences with twists, though I wonder, why you don't check down, down & left, down & right before left and right. I know, it's now similar to SRS, but many things are wrong with SRS, so it is no good reference IMHO. I don't know any common situation, where a down-kick is not desired. Checking left and right first results in some twists only working, when you have more squares filled, which doesn't make sense to me.
In Cultris 2, the S-twist only works in the left picture. IIRC in SRS-style Tetris games it also works in the other pictures, but only if you use the correct orientation before applying the spin.

T-twist only working in left picture:

J-twist only working in left picture:

Another problem is, that some kicks are very unrealistic. I can imagine, stuffing the T and S pieces in a 45° angular into the hole, but how the heck should the blue J piece fit in there?