Sorry on my phone so can't see how old your baby is, but she still sounds young. As a fellow sleep craver, I say do whatever it takes to get you both some sleep. Don't worry about " creating bad habits" at this stage. Do whatever works for you and ignore anyone who can't give you their full support.
A word of warning about sleeping on lounges with babies though (not sure how a sleepy wrap works)
Most all, good luck and sending you and your bubs huuuuge sleepy vibes.