As a linguist I find such community-driven projects fascinating as you can literally see before your very eyes in a time-lapse enabled through an artifically imposed restraint (here in reference to "Old Church Slavonic"; a different approach: Tonki Pona) the language "evolution" and get an humbling appreciation of the multitude of contingences under which languages evolve.
A simplified "linear" scheme I'm referring to:
From perfect "intelligibility" (universal language/Proto-language) --> mostly ("dialects") to limited ("seperate" language) to virtually none at all (seperate "language family").
Of course this gets complicated when e.g. different language families get in 'contact'.
The current Persian language "Farsi" (an Indo-European language, the oldest well-attested Indo-Iranian languages being "Vedic Sanskrit", "Avestan" etc.) is heavily soaked with 'Arabic words' (Semitic language family) through the Islamic Conquest. One of many such examples:
Farsi: کتاب (ketâb) "book", Old Hindi: कतेब (kateba) "book", "Qu'ran" comes from the Arabic root of ك ت ب (k-t-b): "related to writing".
"Arabic" in turn is related as a Semitic language to "Hebrew" which has exactly the same root כ־ת־ב: "forming words pertaining to writing".
The constructed Proto-West Semitic word *katab: "prick, cut, scratch, scrape".
That being said, from a sociologist/ethnologist/historian perspective such artifical constructions are hardly compatible to the cultural complexities in the real world, so mostly it remains a very limited scholarly exercise or it gets "imposed" in order to "stick".
As someone speaking West-Slavic "Polish", learning East-Slavic "Russian" really unlocked for me a big cultural treasury chest which I would argue is even a better pay-off than trying to ideally reconstruct a "neutral" language to circumvent the deep rooted "political" resentments.
As a fun "cognitive"/"evolutionary" exercise, I'm all for it but in order to really appreciate the cultural richness (language as an expression) immersing yourself in a 'living' language is so much "brain-compatible:
(1) Don't obssess over "correctness" and (2) realize the more languages you actually learn the easier it gets to aquire more. (If you speak French and learn Spanish, Latin will connect a lot of things and in the end Italian will be a "breeze")
Transfered to "Slavic" from a "Polish" perspective in learning some "Bulgarian" and "Lithuanian" with my "Russian" in the end you get more bang for the buck. 3 languages are not 3 languages. E.g. "Russian", "Japanese" and "Arabic" would be 1-2 orders of magnitude "costlier".
To sum it all up:
The most elegant and beautiful solution in one's mind ([...] what Old Church Slavonic would have become had it been allowed to develop naturally over the centuries [...]) can distract you from the obivous and the most feasible solution, now, in the real world of "communicating". Just learn the languages "and" at the same time enjoy the beauty of the interconnectedness of languages. There is no pure language, they are all connected, in my eyes: beautifully, as they to my constant surprise succinctly bear our cultural heritages.