Two languages one parent when OPOL feels personally costly

We live in France but I speak exclusively English at work (tenure track professor where most research, teaching and international collaboration is done in English). I'm not a native English speaker and my native language is, let's say Z (hidden for privacy). I have a good accent and can often fool French people to believe I'm non-white American. My fluency in English benefits me a lot professionally. 

And my small one was born and I feel so torn. If I do OPOL with her with my vastly distant minority language, my English and even the frame of mind associated with it deteriorates. She's pre-verbal and I've been alternating between Z and English strictly every day. I'm learning a lot of new vocabularies in English (like frogs say ribbit ribbit) and having a lot of fun. 

If I speak English 50% of my time with her, I expect her to be very fluent in English given my partner and I speak English to each other and we want to send her to French/English bilingual schools. 

• Partner speaks his own minority language and he's OPOL. 

In exchange, her Z will be very weak and most likely she'll end up being a passive speaker (understand but can't speak well). I can occasionally expose her to immersive environments like my immigrant communities or trip to my homeland (12+ hours flight) but not so often. 

But I know some people in my position who tried OPOL and ultimately the kids stopped speaking Z at age 3, 7, etc. So, I'm like, what's the point of going OPOL sacrificing my English? 

Any advice & experience? 

Plus, how will she address me when she starts speaking? I'm curious if she'll say Mama (in English) or Umma (in Z) haha.