Jisho

Troublesome can mean "difficult" so I don't really see any conflict.

https://www.merriam-webster.com/dictionary/troublesome

Hmm, okay. I'm just concerned with the use of those two words in a sentence.

For your reference:

https://japanese.stackexchange.com/questions/60067/difference-between-%E5%A4%A7%E5%A4%89%E3%81%9F%E3%81%84%E3%81%B8%E3%82%93-and-%E9%9B%A3%E3%81%97%E3%81%84%E3%82%80%E3%81%9A%E3%81%8B%E3%81%97%E3%81%84

https://ja.hinative.com/questions/24633

It's OK to use either of them to say "troublesome" "burdensome",
難しい will be more standard/formal like discussing with colleague/yourboss/teacher. e.g. "相談したい難しいところがあります" kinda like "i want to talk to you about this problem here, it's pretty troublesome"
大変 more emotional, less formal. ”今やっているプロジェクトが大変だよ” "the project im doing is soooo troublesome"
This distinction/nuance only work for this meaning, not for other meaning.

Thank you for the detailed explanation.