Hmm. That is an interesting problem. Based on how I understand your issue, FLS is not going to be your best bet. Field level security (FLS) applies to a profile not a user. The more you describe, the less this sounds like what you want. You can watch the video in the link I provided on FLS to get a bettter idea of how they work.
I assume by account record feed posts you mean the FTC (feed track change) that are generated when a field has been chaged. For these, if a user does not have access to a field, they will not see the FTC.
I'm not sure what your best option is going to be here, but it sounds like you have a group that contains a lot more information than any individual in the group would want. What may work better is having account owners collect their own accounts into streams so that they can keep track of their own accounts seperately from the group. The group would then only be used for the @mentions and polls, etc that you described. It is a less centralized solution, but since you want each member of the group to see different data, a less centralized solution may be a good option.
Info on streams: https://help.salesforce.com/articleView?id=collab_chatter_streams_overview.htm&language=en_US&type=0
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