Could you shower together? Talk then?
Ask her to watch all the kids so you get that time for heart to heart connection talk? And you will watch all the kids so they get that chance later?
Hire a babysitter even if you stay in the house and don't go anywhere?
Write letters over email?
That's what it basically what it boils down to. Carve out the time.
Hang in there. Babyhood isn't forever. And the nursing blocks spread out -- I know I felt saner once baby grew larger and eventually was on 4 hour blocks rather than the newborn every hour on the hour thing. When it got to 6 hour blocks it felt like heaven!