While I may not be as fluent as a Deaf person or an adult CODA, I am widely considered "acceptable" by all people I meet. I don't struggle to follow any conversations in ASL, and while my own signing is less than beautiful, it is certainly good. (When I interviewed for a job at the school for the Deaf they asked me to rate my signing skills, on a scale of 1-5, and answer in ASL. I gave myself a 2, for various reasons, that I explained. The Deaf adult argued with me and told me that I was easily a 4.) So, we aren't the average hearing family that learns baby signs and then quits and then can't communicate as their child grows.
We have many reasons that we don't have her in the ASL-English class right now. The first is the silence. The program is totally voice off. A child can use their voice during one, 20 minute pull out speech session a week, otherwise spoken language is equally as forbidden as ASL is in the oral class.
Second, she is not around any fluent spoken language users. Kids learn language best by exsposure to native users, especially other kids. She wouldn't have the chance to be around other deaf, spoken language users.
Third, CI's and the auditory nerve and auditory pathways in the brain are "use it or lose it". If the nerve and hearing sections of the brain are not used, they atropy and become less affective (hence the push for early implantaion) and the window for fluent spoken language begins closing at age 8. (My daughter is 6 1/2) So it is now or never. (If you look at non-users and low preformances users of CI's, you will find very very few that were implanted before age 2, a tiny bit more, but still few, implanted before 4, but after age 5, the number increases rapidly. If implanted after age 8, it is rare to find a fully fluent spoken language user, barring progressive loss or things like that.)
And last, but not least, the school is NOT accepting of spoken language. It is seen as useless, the therapy they provide is inadequate and inappropriate and they don't care. My daughter went to that school, with a moderate loss, and we did all the things you suggested, for 3 years, and she made exactly ZERO progress with spoken language. She started with the spoken language of a 15 month old and she was activated with the same level. Now she has been in the oral program for 6 months and she has gained 2 years worth of language, in those 6 months! She now no longer just has words, but she is getting LANGUAGE from speech as well. For example, I was sitting on the couch and Miss Kat was about 4 feet away from me, playing on the floor (no signs, can't see my lips) and I asked her "What animal has wings AND can swim?" She thought pretty hard, and repeated back to herself "wings and swimming..." and then she got it, "Duck!". So she is not just picking up a few words, she is using and processing spoken language for higher level thinking.
Right now we are doing sort of the opposite of your suggestion. We are emphasising spoken language at school, and doing ASL at home. We have playdates with her Deaf friends, we go to Deaf community events and we attend a Deaf church.