As I have clearly stated above, my example from Tá Mé 'Mo Shuí was not to illustrate this grammar point in particular, but only the general concept that there may be more than one correct way to interpret and express an idea in Irish.
I am not disputing your right to use
ár gcroithe if you wish, only your right to "correct" something that wasn't "wrong" to begin with, namely,
a gcroí.
Since you have asked for proof, Tobar na Gaeidhilge has the following:
Quote:
Máirtín Ó Direáin: Feamainn Bhealtaine
abairt 937, ag toiseacht ar lch 43, líne 18
Ba bheag orthu an fuacht ó bhí a gcroí ar lasadh le grá do Dhia.
Máirtín Ó Direáin: Feamainn Bhealtaine
abairt 2694, ag toiseacht ar lch 110, líne 1
Leis na cianta anuas ó bhí tuatha céadraí ann ba é an teallach croí an tí, agus bhí an tine ina lóchrann teasa, ina foirnéis ghrá, ina laom aitis ar an gcroí sin.
Seán Ó Ruadháin: An Mothall Sin Ort
abairt 1125, ag toiseacht ar lch 78, líne 4
Bíonn ár gcroí briste anois ag iarraidh an turas a chur dínn.
Seán Ó Ruadháin: An Mothall Sin Ort
abairt 55, ag toiseacht ar lch 10, líne 13
Glaine ár gcroí agus neart ár lámh agus beart de réir ár mbriathar.
I have also seen the last quote as "
Glaine ár gcroí, neart ár ngéag, agus beart de réir ár mbriathar.".. It would be a good one by which to remember this formula.