Calm alpaca challenging to halter

Hi all - I have a 15month old female I've been working with on and off the last couple of months. Although she is very calm she is not a "head girl" i.e. not particularly fond of being touched around the head but she does stand nicely and allows ttouches on her neck and then up to her head and around her mouth etc. All good. My problem is trying to get her to accept a halter - one method of avoidance is continuing to move her head up and backwards or to turn her head, which is usually towards me or trying to turn into my arm that is holding the handler helper. I have tried the frisbee with food and the halter and moved it up onto her nose - no problem (except if she isn't hungry, then it's a no go!) I have done that a few times and also fitted the halter which she is ok with - we've even been for walks and she is fabulous on the lead, so all good. Then I try putting the halter on "normally" and she moves her head backwards again. Not wanting to keep doing the same thing I tried something different - as she is fine with just standing I tried holding the halter in my left hand and actually having my right arm behind her neck and then held the halter with both hands and placed it over her nose - she was really good with that method!! There was a slight movement of her neck into my arm, just enough that she realised my arm was there and then allowed the halter to be put on. Now… she is standing in balance, does not try and move away and is calm BUT I have a little Marty bird sitting on my shoulder telling me not to put my arm around her neck
My thoughts were to try this a few times until she is very comfortable with the halter being put on then try and change how we put it on.
I am also very aware that I teach my class participants NOT to put their arm around the alpacas neck but then again I also say not every animal is going to be the same and to think out of the square if it's not working. I probably should not have the students working on her either now - although it's good to have the more challenging ones so they are not all easy
So… am I doing the wrong thing? What do you think?

cheers