Another vote for the "basket stays in the pf" approach...
Each of my two Gaggia Factory machines has a ridgeless/clipless basket that simply rests inside the pf. However, I've found that with practice, I can, in one smooth movement, using the power of centrifugal force (and good aim

), rapidly and smoothly "flip" the pf and have the rim of the basket hit the Grindenstein knock box's rubber bar dead center. For me, this is best done by positioning the point of my elbow one forearm plus pf's length away from the rubber bar, with my forearm starting "cocked", back away from the knockbox/rubber bar and holding the pf face up. I then rapidly swing my forearm in a forward overhand arc, keeping the point of my elbow fixed, until the basket rim impacts, upside-down, against the rubber bar. Anyhow, with the now-upside-down basket between the rubber bar (below) and the pf (above), the rubber bar keeps the basket in the pf for as long as I continue to hold it upside-down against the rubber bar. Usually, the puck exits on impact with the rubber bar (and again, assuming my aim is good, usually inside the Grindenstein...). After that, I can then laterally rotate the pf (with the now-empty basket still inside the pf) 180 degrees by a twist of the wrist, keeping the side of the rim of the basket in contact with the rubber bar as I twist (and moving the pf laterally toward the basket just enough while doing so to keep the basket from falling out) until the pf is more than half way toward being right-side-up horizontal and the danger of the basket falling out is over... All, this is done, btw, without having to touch any part of the pf other than the handle... Practice makes perfect. (But practice far away from windows or other breakables...

)