We believe in one God, the Father All Governing, creator of heaven and earth, of all things visible and invisible. And in one Lord Jesus Christ, the only-begotten Son of God, begotten from the Father before all time, Light from Light, true God from true God, Begotten not created, of the same essence as the Father…
To appreciate this we need to consider for a moment or two what Christian creeds and confessions are. They are not Scripture, of course, and they are at best subordinate standards. They set forth a ‘system of doctrine’ (as in the WCF) or part of that system (as the Nicene Creed sets forth a fundamental part of it.)
So much is clear. (To me at least!)
Those who subscribe to the WCF do so in terms of the 'system of doctrine' that the document sets forth. Does this help? Did Edwards and Sir William Hamilton subscribe to the same system of doctrine? I doubt it. A libertarian interpretation of 'contingent' 'free' 'liberty' is on the way to claiming that the WCF contains another system of doctrine than a necessitarian reading. Besides, that phrase 'system of doctrine' is itself somewhat opaque.
Where names have not been invented rashly, we must beware lest we become chargeable with arrogance and rashness in rejecting them. I wish, indeed, that such names were buried provided all would concur in the belief that the Father, Son and Spirit are one God and yet the Son is not the Father, nor the Spirit the Son, but each has his peculiar subsistence. (Inst. I.13.5).
So, if what you are interested in in subscribing to a document that is intended as an expression of unity and concord, better to stick to the very words, and to keep your further understanding to yourself. If you don't, and expect your words to be tolerated, or officially endorsed, someone else will surely ask for his further understanding to be tolerated or endorsed. Better that explanations are treated as mere private or personal thoughts, 'just the opinions' of those who give them, don't you think?