We used to NIP all the time when we used the LA. I wore a t-shirt over top of a tank top with a built in shelf bra. I just discreetly dropped the bag into the space between my boobs, aimed the tube (still pinched off) at the boob I'd be using, put the baby into position, lift the t-shirt, pull down the shelf bra exposing the nipple, position the tube with my thumb and finger as baby latched on, and then released the tube with a gentle tug. Sounds complicated, but the whole process took less than a minute. If you need to, you could pop into a bathroom to get set up. I did this sometimes.
We even did this in the ergo carrier too ... the trick was loosening the side straps so that baby hung lower.
ps. We never taped.