This isn't a direct response to your post and neither am I trying to rebut anything in particular, but on the topic of the profession of faith, I found this quote from Robert Boyd really interesting and possibly worth thinking about. I found it from Witsius quoting him in the publication
On the Efficacy and Utility of Baptism in the Case of Elect Infants Whose Parents Are Under the Covenant, as translated by William Marshall and published in the Mid-America Journal of Theology, 17 (2006), 121-190:
The part in bold interests me as I don't think I've ever seen it stated so boldly as that before.
The reference of Boyd is below.
It appears that the text is in Latin, so unfortunately I could not find a translated source online.
Robert Boyd, Roberti Bidii A trochoregia Scoti SS. theologiae in academiis salmuriana, glascuana, & Edinburgena professoris eximii, in epistolam Pauli Apostoli ad ephesios praelectiones supra CC. lectione varia, multifaria eruditione, & pietate singulari refertae (London, 1652), p. 762.
Edit:
Here is the link to Page 762.