Tom Klein writes
"either King David's line ended, and no one is, or after 1000 years everyone was his descendant"
The theory that everyone's family branches out indefinitely is  fallacious.  In any population, the number of families available to marry into was restricted by limited
possibilities of travel  and limited communications - far worse historically  than.in modern times.  Custom, too,meant that cousin marriage was usual, particularly in the upper and wealthier classes.   Limited knowledge meant that local records often aren't specific enough to provide reliable proofs,   based on calendars and place-names which differ over time and and may  even be subjective.. However,  only  an estimate of number of descendants is wanted, one could work ones way through the Bible from Samuel onwards and follow the generations as they are enumerated, extrapolating from there.. You don't say whether you are counting only the male lines or also the female lines, which aren't available, of course.Also there was quite a lot of 'marrying out' during the Exile in Babylon,  and those lines, too would be ignored thereafter.
Eva Lawrence
St Albans, UK.