Maybe you could tell your parents you're going on a weekend trip, rent a place with a fireplace for a day and do it there?
I'm living in europe in a biggish city and I slept in forests in and around the town and never encountered people at night, so I guess it would still be weird to do it there, but possible without meeting people.
How would one actually do it in a tent? fire up a grill? how would one make sure that one doesn't set the tent on fire or when becoming uncouncious falling onto the grill? tents are usually small :D
You slept in forests? Amazing! Can you give me advice? It will save me hotel cost. In my country there are hundreds of lush green forests and mountains (south asia).
I myself have decided to roam alone in the northern areas of my country, I have been feeling so miserably suicidal that I don't care anymore if I enrage my parents at this decision of mine, I'm abandoning everything one way or the other.
On the bright side, doing CTB hundreds of kilometres away from home feels soothing, it will spare my parents the sight of gruesome corpse of their firstborn.
To the OP, one has to allow oneself the fear of death and the extreme agitation of survival instinct, and weigh all this against the hurt one might cause one's family. For instance, I often go to the rooftop of a 25 story building right besides my residence, and I contemplate the final jump, it will be certain death as there is hard concrete below. I keep the sight of my dead body clear in my mind and think about every person in my life who will be affected by the sight of this corpse.
And then I think about a roundabout way of CTB, that of abandoning my family and living in the cold climate of mountains for a while, just to plan my CTB.
Now, unless I've actually reached that place, I cannot predict my state of mind there as compared to here with my family (my family depresses me extremely).
I hope I have been able to explain myself, sorry for the long paragraph.
Tl;DR : Death promises eternal non existence, neverending deep sleep without dreams, it's promised. Forever will you be unharmed in the void. Might as well give yourself some peaceful solitude away from parents for a while. Who knows, you might even figure out a palliative to your problem (I hate to sound like an optimist).