If you have links to the school of thought you mentioned, I’d appreciate them.
It does not alarm me at all that the Tel Dan Stele is 150-250 years later than David’s time – since it was referring to a conquest within the “House of David.” I looked at the museum site to find anything to support your remarks about their position, but couldn’t find anything.
I did find this good summary of 3 archeological references to the House of David. For the discussion:
This is the third possible mention of David in ancient inscriptions. The clearest reference is in the much-heralded Tel Dan inscription from the ninth century B.C.E., which refers to the "House of David" (bytdwd, or Beit David). Carved in Aramaic on what appears to be a victory stele celebrating the victory of an Aramean king over Judah and Israel, this inscription was found in 1993 by Israeli archaeologist Avraham Biran.
The eminent French paleographer André Lemaire has also detected a reference to the House of David in the long-known but still not completely deciphered Mesha Stele (also called the Moabite Stone), which is contemporaneous with the Tel Dan Stele, although this reference to the "House" is based on an unclear reading, and the reading of "David" is based on a highly probable reconstruction of the initial letter of the name.