The following is a major revision subsequent to more study and research:
The tent of David was a partial copy of the Tabernacle. The original, built by Moses, was maintained at Gibeon minus the ark. Saul had it moved there from Nob after he had all the inhabitants of that town murdered. The original Tabernacle was moved from Shiloh to its previous location at Gilgal after the Ark of the Covenant was captured by the Philistines. The town of Shiloh was obliterated by the Philistines soon after.
When the Philistines returned the Ark it never caught up with the Tabernacle! Even when Saul moved the tabernacle from Gilgal to Nob, he did not reunite the Ark with the Tabernacle. The Ark was stored at Kirjath Jearim on the property of Abinadab where it was cared for by his consecrated son Eleazar according to 1st Samuel 7:1. Verse 2 records that it was kept there for twenty years which may have been when that verse was written. It was clearly there much longer than that (nearly 80 years) because that is where King David retrieved it from in 1st Chronicles 13 during his first attempt to bring it to Jerusalem. David stopped short of taking it into Jerusalem because of the untimely death of Uzza who mishandled the ark on the journey. It was left at the home of Obed-Edom for three months according to 2nd Samuel 6:11. David had completed a partial copy of the Tabernacle in Jerusalem to house the Ark and a team of Levites transported the Ark properly to that location. It seems that the Ark remained in David's tabernacle until completion of Solomon's temple. Solomon's coronation occurred at the Moses Tabernacle 2nd Chronicles 1:1-6. Construction of the temple was started four years later.
The decommissioning of the two Tabernacles is apparently undocumented. Deteriorating fabrics were possibly trashed and recovered metals returned to the treasury.
A better alternative may have been designed into the Temple structure by Solomon as extra rooms to store the Tabernacle components as religious/historic relics. It was likely within these extra rooms among these items that the Book of the Law could be misplaced and later found by Hilkiah during the reign of Josiah according to 2 Kings 22:8. Without all these items being stored within the Temple structure how could the Book of the Law possibly get misplaced?