I would be very grateful if someone could provide a competent opinion on this matter, or share contacts of authoritative experts who can provide an independent assessment of the situation.
I am not sure if any of us who contribute to this Web site would claim to be "competent" on these matters - interested - yes; knowledgeable - well more than your average person probably, but, speaking personally, not "professionally"!
I would start with ICOMOS which is the body used by UNESCO to adjudge Cultural nominations for World Heritage. They do far more than just act in this role for UNESCO and are involved in the protection and preservation of monuments worldwide.
There is a National Committee of this organisation in Ukraine see - http://icomos-ua.blogspot.co.uk/p/blog-page.html
I cannot speak for whether this Committee escapes or is tarnished by the sort of political views of which you talk - but, through them, you should be able to gain access to International papers and experts - But I would find it amazing if they were not already involved in this matter. A few links http://www.enamecharter.org/principles_4.htmlhttp://www.icomos.org/centre_documentation/bib/Biblio_authenticity_2010.pdf
You might also find it of interest to follow up on the subject of Bagrati Cathedral in another ex-Soviet "province" - Georgia. This IS a World Heritage Site and Georgia (or elements within that country) decided that it should be restored. ICOMOS/UNESCO have not been exactly pleased with the result! Here are a couple of links to start with -http://en.tabula.ge/article-6673.htmlhttp://archaeolaw.com/2012/01/11/unesco-pressures-georgia-to-revise-restoration-plans -on-medieval-cathedrawl/
The UNESCO inscribed city of Yaroslavl has also been involved in rebuilding religiuos buildings destroyed during the Soviet era. The project was pushed trough by a local "oligarch" who happened to be in the construction business!! Look up "Dormition Cathedral Yaroslavl"
As you may be beginning to appreciate, on these matters there is unlikely to be a single opinion even among experts!!