Items/tools needed: 2 rubber bands, your hands

STEP 1. Loop the rubber band behind the plastic piece that controls height adjustment:

STEP 2. Stretch it up top and loop it around the plastic piece next to the hose:

top view

Repeat Steps 1 and 2 for the other side
THAT'S IT! .. If you tuck it securely around the top plastic piece, it will not move and stays put. Every piece of the headgear is accessible (you can remove the nasal piece for cleaning without disrupting the elastic setup).
Best of all, only the nasal pillows touch the face, no extra straps or steps for your nightly routine.
Edit: Oops .. links repaired .. redirected pics to new site .. thanks Ozij and RG for helpin out!
Edit: In case anyone is searching, modified the subject to reflect correct name (AEIOMed Twilight NP). The newer nasal piece is much better and may not require this trick anymore!