Should I tell my situation or request a possibly negative recommendation letter?
"Too busy" means "I won't write a letter you'd like."

"Describing conflicts" with your supervisor will raise flags you do not want to raise.

Your choice 2 is the correct one.  If you are asked why you don't have a letter from a current faculty member, say your working relationship with your thesis supervisor was "difficult."  Do not say anything more except to answer further questions as briefly and politely as possible.  Let your transcript speak for itself.