Two questions:
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Where did your brothers go to school and did they like it?
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Would you be open to attending other schools?
You have said it yourself - the acceptance rates for these two schools are low. Groton in particular probably has one of the lowest acceptance rates of any boarding school (8%-9%) in part because it is the smallest school in the top tier.
As others have said, if you are truly interested in the boarding school experience, then I would cast a wider net.
In my estimation, none of these schools are particularly religious and they all generally welcome students of any faith; I would not be worried about that at all (one person’s opinion). I would again be interested in where your brothers went and whether they (if applicable) felt out of place at a non-Catholic school.
Also, to answer your last question: applying early does not give any measureable advantage.
Best of luck!