So, I've been working on this in my survival world, and I wanted to share it with everyone. I started with ilmango's design, which was broken when the game was updated so that phantoms now only drop membranes when killed by the player (also they don't drown any more). This means that instead of killing them, we need to collect them.
Brief outline of the mechanics:
This farm uses the mob AI to direct the phantoms into a killing chamber. When phantoms attack, they swoop in at about the head height of the player, then fly straight up to come around for another pass. This design tries to force them through a tripwire, which triggers a sticky piston to retract the entrance to the killing chamber. The AFK spot is directly beneath the piston, since the game treats them as transparent blocks.
The killing chamber itself uses Enchantment Tables to create a gap through which the phantoms can be seen, but that they can't get through (my initial design used slabs and I died VERY quickly!) They can then be killed with a Looting sword to maximise the drops. You can place a button somewhere along the redstone line to manually open the killing chamber, causing the membranes to fall down to the hoppers below.
I included an AFK fish farm in the version I built in Survival - Docm77's new design is only 1 block wide, so fits nicely into the AFK zone. I should also note that yes, this farm only works if the phantoms attack you from one side - in my survival world I built this next to a large building so this isn't really an issue. I'm sure this can be improved on though.