I'm not sure how the deck adjustment is set up on your mower, I run the Pro-Master series, but I do know the actual cutting height is usually set by the dealer. I had one mower, and a few years later added another. One deck was a half inch higher than the other. On the older mower, the mechanic that assembled the mower simply set it up wrong.
As for the deck lift latch not working, I don't have a clue. I don't understand how adjusting the height would effect it.
Dependable Mowing Service