Getting baby out of sling for naps

[Gargula]

Hi,
Since my DD was born she has napped in a sling. She is now 5 months and I'm getting a little bit tired of having to carry her for each and every nap (often having to feed her off as well).
She naps NOWHERE else. She hates being in her pushchair or carseat - doesn't mind her cot at night but she is fed to sleep then as well.
I just don't know what to do. I'm not prepared to let her cry and I can't dedicate time to this "problem" as I have a demanding 2yr10 month old as well.
Will she ever grow out of this - or will I actually have to do something?
DS starts preschool in a couple of weeks but only for two mornings a week so I could start trying to put her down for naps then.
Sling users - when did your baby eventually settle elsewhere??

Which sling do you use? Just wondering how easy it would be to ease her down onto a bed or summat stil in it. I've done it carrying front and back, in a wrap, ring sling and mei tai...

DS naps in a sling when we're out, but indoors he'd rather stretch out on my lap to be fed to sleep. Then I move him onto whatever piece of furniture we have around that he fits. Once a hammock, then a car seat, bouncy chair, travel cot etc. If I wait about 10 minutes he rarely wakes.

Would your DD fall asleep on your lap? Probably not a long term solution but could help break the sling habit?