What I'm about to suggest might be troubling with another (very) lo to attend but it's doable. PRobably her resistance for sleep has to do with the switch from couch to bed but also with some separation anxiety due to her age and the arrival of little sibling. She might feel she needs to be awake so she won't miss any special mommy time, kwim?
If Caroline's (PP) suggestion is not doable or won't work (cause that would be my first suggestion) you might try and make nap time a special cuddle time for her, like I'm gonna stay with you for a long time and read books (or sing songs, or tell stories, or play with dollies) with you but then we have to go down for a nap. That way, she gets her special mommy time BEFORE the nap and she'll get relaxed and ready for it and will associate her bed with daytime sleep as well. In case she doesn't go to sleep, at least she'll take the quiet time ok cause she has already spent quality time with you, so she won't feel she's been abandoned or being left out.
The timer is a great idea, some moms here have night ligths with timers (if noise is an issue for you) where the light goes on at the desired time. You can tell her she can go out of her room when the light's on cause that's waking time. Probably the first couple of days she won't nap (or will take long time to finally fall asleep) but once she gets the handle on how things work, she'll hopefully be on board for it.
Also you mention you'd do pu/pd if she were in a crib. But what about trying Walk in/Walk out (which is sort of the modified version of pu/pd for toddlers?). You'd lay her down say night night see you later and walk out (wo). She cries (important: not whine or moan or chat, you just respond to the cries) so you walk in (wi), reassure briefly, say night night again and wo. Keep doing that until she stops crying. If she's ok once you wo then leaveher be even if she's not sleeping. She'll go to sleep when she's ready and if she doesn't associate her nap with a power struggle or a stressing time.
I hope this helps you. Congrats on your newborn sleeping through! Good luck!