Hi there and welcome

It could help to have a look at your full day routine of EAS times as sometimes the routine is not quite right for LO and that can lead to it being harder to wean shush/pat. If you could post your times as they happened for a full day and night we could have a look.
Otherwise, the weaning aspect needs for you to keep your goal in focus and stay absolutely vigilant to LO as she is falling to sleep. It is easy to get into a rhythm ourselves and kind of just go along with shush/patting and kind of get carried away with it, especially when we are tired and especially when we really want LO to sleep and not wake up or delay the nap, this can lead to habitually shush/patting all the way to sleep for an easy life rather than moving on from it. You can expect LO to be a bit frustrated now that you want the habit to change. To wean shush/pat you would need to take the risk of the nap not being 100% perfect, she might not go to sleep right on time whilst you teach her that it's okay to go to sleep after being patted an that she doesn't need it throughout the falling to sleep phase.
Every wind down you would begin as normal, what ever you usually do. Then you'd put down in the cot and do the same rhythm and pressure of shush/pat you usually do initially. But then instead of continuing in that hypnotic rhythm you change it up. Do a bit of on off and stop start, each time you stop it is brief and just before (or as) she starts to get a bit fussy start again), change the pressure as well as the pace. Reducing the weight of the patting and then increasing to the normal pressure, then reducing again.
Staying vigilant means that you will notice when she is calm and relaxed and this is cue to reduce reduce (more off than on, less pressure more stop than start) but always increasing again if needed...and ultimately aiming to be hands off as she nods off. If you cannot be hands off you make sure you have stopped patting and only using a still hand, very small soft pats occasionally if needed.
if she kicks up a fuss you increase and go through the whole thing again.
I know you said if you stop earlier it is even more difficult to get her to sleep but that's what you'll need to do and with the second or third round you keep focused on reducing when she is calm, just as before. She will eventually nod off with your hands off.
From there you can either do a gradually withdrawal from the room or after a couple of days go for a full walk out, using a full wind down as before then when she's calm and sleepy and you can stop patting just say "sleep well call if you need me" and lave the room. Wait outside if you like. If she cries go right back in without delay and shush/pat again, repeat.
Personally I think it's worth a few days or a week if some disruption because it's so lovely to know your LO is happy to go to sleep alone and has full confidence in your returning when needed. I can still remember my LO smiling at me when I put him down and I would say my phrase and wake out. It was lovely to know he was so happy.
hope that helps