First things first - DO NOT attempt to cut the strings yourself, this needs to be done by a professional and with a speculum in place.
The strings need to be a certain length so you are able to check the Mirena is still in place. (Also, if they’re too short, the strings can curl up on themselves and disappear inside your cervix which makes for the most excruciating removal when the time comes. And believe me, I speak from experience of this.)
If you feel they are too long and the practise nurse won’t help, go to a sexual health clinic, one where they also provide this kind of contraception service/fit IUDs, and have someone there trim the string for you. If you’re in London, I can recommend the clinic on Leadenhall St in the City (it’s where I used to get my IUDs). it is also worth remembering that the strings will soften after a few months. Additionally, it might be your cervix now sits lower which will make the strings seem longer than they possibly are. It might also explain why a few of your clients can feel the strings.
With regards to your clients - just ignore their ridiculous comments (it is incredibly rare for an IUD or Mirena to simply fall out) and if you don’t want to take fingering off your service list, tell them to be more gentle.
I’ve had IUDs for the best part of twenty years. I don’t think anyone has ever felt the strings or commented on them.