The articular infinitive is fun, isn’t it? This may be the most common construction in the Koine Greek that is has no real English equivalent. I’m a little confused about the way the sentence was parsed by your friends in the first paragraph, but I’ll explain it as I understand it and perhaps that will be helpful.
καὶ νῦν δόξασόν με σύ, πάτερ, παρὰ σεαυτῷ τῇ δόξῃ ᾗ εἶχον πρὸ τοῦ τὸν κόσμον εἶναι παρὰ σοί.
The part in bold contains three elements:
- a preposition (πρὸ = before);
- a genitive articular infinitive (genitive article = τοῦ; infinitive = εἶναι = “to be”); and
- an accusative articular noun (accusative article = τὸν; accusative noun = κόσμον = “world”).
This is a form of temporal adverbial clause. The construction prep. + gen. art. inf. (1. + 2.) is usually translated “before + finite verb”. The accusative noun nearby (3. – here, confusingly for the English speaker, introjected between the article and the infinitive it modifies), can function as the subject or object of the verbal idea. The copula εἶναι doesn’t take an accusative object, so "τὸν κόσμον” is the semantic subject of the idea contained in the infinitive. The basic translation of the bolded part, then, is:
before the world was
The sounds a bit odd in English without a predicate, so it’s often re-stated:
before the world existed
The final prepositional phrase hanging onto the end of the sentence παρὰ σοί (“with you”) is also modifying the finite verb (“I had”). So we have:
the glory that I had with you before the world existed
The translation you offer:
the glory I had, being with you, before the world
isn’t substantially different in meaning as far as I can see. However, the “to be” verb is really part of the adverbial clause with the subject, “the world”. It is misplaced in this translation.
Please note that word order is almost irrelevant in this analysis. I think that may have been what threw you off. The syntax is determined by a very well-defined collection of elements (1. + 2. + 3. above). We re-arrange the words in English however we need to in order to convey the idea.
A discussion of this construction can probably be found in any introductory or reference grammar. Two examples:
1. Wallace, Daniel B. Greek Grammar Beyond the Basics: an Exegetical Syntax of the New Testament (Zondervan, 1996), p. 590ff.
2. Smyth, Herbert Weir. Greek Grammar for Colleges. (Cambridge: Harvard University Press, 1918), §2032.