I'm sure that we agree, our trust should not be in the Jews, but in the God of the Jews.
Absolutely, our trust should be in God's testimony to us in all things... for which it discusses. Now it does discuss this matter of the passage of time throughout His account in various genealogical records, and various pronouncements of ages at births and deaths, but, as some of your evidence does suggest, there may be small 'accounting errors' over the course of 6,000 years. I, like you seem to, put some value in the 6 day as a thousand years 'theory' of time as it unfolds to the end. The day when Jesus will be established to reign as king for a thousand years with those who have trusted in him. I'm also sure that it will come whether I'm ready for it or not, but looking into the matter is worthwhile as we glean some of the 'weightier matters of the Scriptures'.
So yes, I've often given great weight to 'evidences' that come to us through the Jews concerning the things of God. I don't buy into John Smith's story about golden tablets as a worthwhile claim of evidence. But when the Jews, who while I absolutely agree struggled to keep God's law, have worked out a timeline of their own historical record to be 5, 784 and another group who studies the matter says 6,025, and I'm expecting something to happen around 6,000?, I want to know who's correct!
In this case, obviously whatever was expected didn't happen at exactly 6,000 years, and I'm ok with that if it happens fairly soon. But if it's still 220 years away, then it's not something I'd be looking particularly hard at to be happening while I'm living, anyway. And of course, all of that is tempered with the understanding that the 6 day for thousand year 'theory' could be wrong.
I believe that Jesus did warn us of other signs that we would see besides just a count of days. But it is certainly a time in which we should be looking up for the day of our salvation draws near.