I am concerned with what we are taught by scripture. Your reference in Gen and Exodus deal with the six days of creation and the Sabbath. On these matters, we have a clear understanding from scripture.
I cannot understand why you would deal with this on the basis of what the Lord wants us to be concerned with - He wants us to obey His commandments and to live according to the Gospel. Issues such as dates of the earth, and similar matters, seem to arise from our own arguments.
I see the commandment to keep the Sabbath as central - from this, like you, I ponder on how we can obey that command. My reasoning is along these lines - if we are to keep a specific period of time that God sanctified as His Sabbath, than the bible would have provided clear data that would enable us to do that. If not, than the Sabbath is the day after our six days of work, and we would create a calendar that was faithful in those terms.
The exact period of time that corresponds to the Sabbath in Genesis (to follow your reasoning) MUST be calculated by having an exact chronology commencing with day 1 of creation, followed by 2, 3, etc., until we have the exact period that is the Sabbath. Once we have that, we would create a calendar to ensure these periods were known to Israel and nowadays, to Jew and Christian. In this way we would keep the exact period for the Sabbath, and know the years that have passed since Adam. No ambiguity, no interpretation, would be needed.
I give these details because keeping the Sabbath is one of the ten commandments. I cannot think of anything more important then the 10 commandments - Christ came to fulfil the Law and the prophets. If a chronology commencing with Adam were required than I am certain the bible would provide this and we would not be having these lengthy discussions on an age for the earth.
From my school days, I seem to remember that the Jewish calendar revolves about the sun and moon, and the Sabbath and other Sabbaths (holy days) were calculated in this manner. Correct me if I am mistaken, but this calendar varies considerably, and I cannot recall a biblical passage that enabled Moses to make an exact beginning (from the first day of creation), or the first Sabbath, or any other point of reference.
As a result there have been a number of attempts (if I recall this correctly) at devising calendars, and none can clearly start from day 1 of creation. Thus I conclude we do not have a clear biblical method, or some dating, or command, that enables us to determine the age of the earth.
As a result, some may turn to science (and associated controversies), others to history (and errors as we go back further) and others to inferences from biblical sources. All indicate some personal preference - none are based on a clear biblical teaching.