I used the co-sleeper you linked to for the first few months of my daughter's life until she outgrew it (length) and I just let her sleep in the bed with me. I was a pretty sound sleeper pre-baby but that changed once I was breastfeeding.
It wasn't an issue for me to lift her out of it (the sides are only a few inches) but I didn't master nursing while lying down until she was a toddler

...so I was sitting up in bed every time she wanted to bf anyway. The sides are actually low enough on that one that it would probably be possible to just lean over the baby to bf. (I think I'm due a few weeks before your DP so I can update you in October if you'd like.)
I really like the co-sleeper in your link. If your DP is going to be the primary breastfeeder I'd probably just go with that one and let her do most of the night nursing if it's difficult for you to lift the baby? Or an alternative would be a sidecar co-sleeper arrangement (again having your DP do most of the night feeds) on your DP's side of the bed. I know neither of those are really ideal, I hope someone else has a brilliant solution. Maybe try cross-posting in breastfeeding or nighttime parenting?