6 week old not happy in the sling

[duende]

DD will be 7 weeks on Friday and I have been trying her in the moby sling for the last 4 weeks I think but she is just not happy in it.
I've been putting her in the hug hold position with her legs out (legs in was a complete no-no) and she starts moaning after a few minutes and then just gets annoyed. She also licks my neck and chest every time she's in it, even if she has just been fed, so I always end up having to take her our and feed her again.
She likes being hold upright, tummy to tummy on our shoulder so I'm really disappointed she's not happy and napping in the sling. It would make afternoons and evening with her and 4 year old DS much easier.
Any words of wisdom?
On every thread about a colicky/ unsettled baby someone recommends "just out her in the sling and she'll sleep and you can get on with stuff" but my DD doesn't seem to have read these threads....

What do you do once she's in the sling? My DS (15w) has been going in the sling since he was about 2w but will only tolerate it if I'm walking outdoors. Indoors he'll last for about 5 minutes (10 mins tops if I'm actively swaying/bouncing), even if I'm moving around.

Especially in the early days he'd really struggle against the sling, leaning backwards, moving his head backwards (if it was covered, I'd have to support his head with my hand, because he wouldn't tolerate the fabric). I do think he's got used to it more now, as I only use a sling, no buggy/pram, so he'll occasionally go to sleep in the sling. But yeah, only when out & about.

He does the licking thing too, I don't think it necessarily means he's hungry. I'd only take him out to feed if he was actively rooting.

I have a toddler and would also love it if DS2 would go to sleep in the sling while I get on playing with DS1 or putting him to bed, but I guess like your DD he didn't get the memo either