Instead of the 1,776 gold that the quest said was the reward, I was given a single chest.

You are correct.  

 

There are a handful of reason why the mismatch has occurred, but there are indeed a bunch of bugged weekly challenges.  

 

I wish I had something else to tell you, but if you're willing to drop an email to support@obsidian.net with your PFID# (found at the bottom of Pathfinder Options --> Settings) and a brief description of the issue ("The 4th of July weekly challenge did not reward the expected 1776 Gold, so some user on the forums said to email you."), customer support should be able to make things right.

 

Sorry about that.