Honestly people are ridiculous, as a PP has said, keep it consistent, soothing but boring! For some gradual retreat works better (you being in room to begin with) for some not being in the room works better as you aren't a distraction. Mine got restless if I was in the room, if I left, asleep in 2 mins, no crying.
I never understand the crazy reaction to this, it's not just closing the door and leaving the baby for hours screaming, you check on them at frequent intervals so they do 'know you are coming back' but they know that when you do come back it's just for a quick bumpat and a 'its bedtime sweetie, night night' rather than a full song and dance breastfeed, self flagellation entertaining performance.
They then realise that bedtime is for sleeping not playing/eating and get bored and fall asleep, then when they wake up in the night they know it's fine to go back to sleep.
It's like dropping a kid off at childcare, people who work in childcare know that 9 times out of 10 once the parent is out of sight out of mind the child stops being upset and that long protracted goodbyes and rituals make it worse. If you applied the same insane response to childcare drop off as people do to sleep training you would just have nurseries full of parents hovering next to screaming children (and frustrated childcare workers just wishing they would all fuck off so they could get on with their day)
People act as if their kids don't cry EVER if they avoid sleep training, it's BS there is no such thing as a child that doesn't cry at some point, if they cried and tantrummed for 20 mins over a chocolate biscuit would you give in to them if you had already said no? If not then by this logic surely that's 'child abuse' too, 'I could NEVER leave my child crying without a chocolate biscuit, those poor kids in Romanian orphanages were silent as they weren't given chocolate biscuits the second they asked for one.' Give me a break.
OP you do you, would recommend properly following a set system and being boring rather than being inconsistent and making it up as you go along. They shouldn't be getting to the point where they are sick, I think your presence in the room is probably making it worse rather than better, good luck and don't let the crazies let you feel bad, thousands of parents do this and very quickly end up with well rested children, they are well rested and get quality of life back, rather than being cling-martyrs who can only make themselves feel better about their chronic sleep deprivation by shouting at people on the internet!