For W2S, the goal is to get LO to stir and start a new sleep cycle. I tickle DS behind the ear or if that doesn't work, I scratch his ear. You just want them to stir a bit but not wake up!
For the 20 min naps, could it be that DD is having trouble transitioning from light sleep to deep sleep? I believe it takes 20 min for them to get into deep sleep. Maybe even try httj at 20 min?
With my DS, he will stir a few times during the first 20 min, and sometimes his eyes even pop open. DS doesn't fall asleep independently yet, so I have to hold him to sleep for 20 min before I put him in the swing. If I want him to sleep in the crib, I try to put him down when his eyelids get heavy and I start shush/pat. After a few min of his eyes being closed, I just pat, up to 10 min, and then I hold my hand on his back for the next 10 min. I don't let go until just after 20 min, as he sometimes will stir/eyes pop open after 5 or 10 or 15 min and then I start shush/pat again.
HTTJ isn't working perfectly for us. I tried a nap yesterday with just httj starting at 25 min, but he still woke up at 32 min. I didn't do W2S, so I will go back to doing both.