Avira –
The scholars I suggested (Halbertal, Kreisel, etc) do not tell people how to pasken, nor they tell people what to believe or what to do.
Rather, they present evidence to help people to better understand things.
The one academic author who does address halachic aspects and does write about the Ikkarim using both academic and halachic methods is Rabbi Prof Joshua Berman, whose Ani Maamin: Biblical Criticism, Historical Truth, and the Thirteen Principles of Faith is published by Koren and has been widely reviewed and discussed by Orthodox Rabbis and scholars all over the internet.