I have been doing waxing, using strip wax on brazillian and hollywoods for years.I was trained in hot wax but the salons I worked in didn't use it so I continued using strip wax.
I have never had an issue with warm wax only working on clients with previously waxed hair,I have done wax virgins and got perfect results(total hair removal,no problems)I think it's because the hair needs trimming that there is an issue here,if the hair is too long it will end up clogging in the hair,whereas you are getting good results on previously waxed hair because it is shorter.So it definately needs trimming.
Recently I did a new advanced training course(using non strip wax)because waxes had changed hugely from being very hot to not as hot as warm wax but designed to be a lot kinder on the skin.So I thought I would give it a go and I couldn't believe how there was no redness to speak of and how my model said it felt so much more comfortable.
I can get the same result with either non strip or strip though because I have been doing it for years and it's mainly imo down to experience and technique.
If the hair is too long I would suggest you either ask your client to trim it or you trim it prior to waxing.Really press the strip onto the wax,rubbing the strip hard back and forth,and you should get a good contact and then be able to remove all the hair.Keeping the skin taut all the time is crucial and prevents bruising(get the client to help with holding the skin)
Have you thought about speaking to the owner and asking if she would mind you using hot wax instead?(if you prefer it)It does take a lot longer than strip waxing but your treatment costs will reflect this so it shouldn;t be an issue.HTH a little