“I hate to use a hackneyed expression, but they are rearranging the deck chairs and the ship is still sinking,” said John Wells, a retired Navy commander and lawyer who runs Military-Veterans Advocacy, a nonprofit.

The main cause of delays, according to the department, was a design flaw that fed appeals with simple errors into a legal system that was meant to rule on complex cases. That led to thousands of cases with issues as small as a typo clogging up the flow of cases to be processed.

“We tried to do everything in one stream and it couldn’t work efficiently,” said David McLenachen, who leads the department’s benefits appeals office.

The new law triages appeals into three streams: A fast stream — like the express lane at a supermarket — to correct simple errors; a medium stream, in which a more experienced department specialist reviews more complex issues at a local level; and a final stream where veterans can take cases to an independent board of appeals. The agency plans to hire hundreds of additional claims processors with the goal of clearing each case within four months.

But lawyers who represent veterans say the changes do not address the core problem: The department’s vast number of errors, which have generated hundreds of thousands of appeals. A 2017 report by the Government Accountability Office found nearly half of cases were plagued by mistakes and reached the Board of Veterans Appeals — the final authority for veterans benefits cases — only to be sent back for fixes.

Cases that have been sent back can sit for years before they are addressed, then sit again as they wait for the board to read the revisions.

Making a fair ruling on injuries of war is far from easy, and veterans advocates say some cases will inevitably take time to sort out. But as Mr. Bey’s case shows, even simple issues can languish, and recent changes by Congress have so far offered veterans like him no relief.