Let's start at the beginning:What methodology would you recommend? The blu-ray is so far off from the 35mm it's hard to dismiss it as minor variations in screen capture or bulb temperature. However, I'm open to suggestions because I think this is very important.
How are the captures created?
Is there any compression happening following scanning?
Has any manipulation occurred following scanning?
What colour space is being used?
When doing the comparison screen caps, what software are you using? This is important, as some software players are known for having colour issues?
While you have indicated that you cannot disclose whose print this is publicly (and I completely respect that) you should be able to answer some of RAH's questions about film stock and production date, etc. from the edge coding on the stock.
Let's start there, and then we might get somewhere.