My DD was like that, so I ended up wearing her in a woven wrap so I could get stuff done. My wrap is an EllaRoo brand, but you might also like Wrapsody gauze wraps (now that it's warmer in our part of the world ... happy April!) or a Didymos.
Another suggestion would be a linen mei tei or ring sling ... I'm up to my eyeballs in warm weather babywearing suggestions right now with my babywearing group.
There's a group that meets in Central Park that might be a good fit for you; they're called the Carry On Baby Babywearers. Their FB page is: https://www.facebook.com/pages/Carry...21595484524104
You're not doing anything "wrong" and Miss Mopey will be just fine if you snuggle with her a bit more. FWIW, wearing your baby "counts" toward tummy time.