Why does it take forever for DPS/TSP to complete and send a check for your claim for broken or missing HHG?

To give a more serious answer -- I think this is just another byproduct of a DoD system that has no real pressure to improve over time. There is such little accountability and people can easily be lazy and face no ramifications. There is no basis to have a system that takes 6 months to refund your money if movers break your stuff. This is just waste and inefficiency -- and frankly it's embarrassing that this is called 'the standard' in the military.

My man, this is one of the answers we will all have to ask the good Lord on that special day we meet Him. ;-)

My wife and I were always "up in their face" when it came to claims from moving. I retired after 21 years, and we moved almost every two years. We didn't have to file claims every time, but we always made sure they knew we wanted to get compensated for our losses. Average time for payment was still 3 months or more. The key is to 1)make sure the moving company knew who you were and that you were serious about getting the claim done in a timely manner, which meant that 2)you have to call them weekly to check on the status of the claim. And if they couldn't be reached by phone, sometimes showing up at their work made them suddenly easier to reach.
Understand that DPS/TSP is not who pays you for missing or broken items on a move. The actual movers are responsible for costs incurred due to a move. Find out who the movers are and put all your effort where it belongs.