Step 1)
Locate the save folder, the easiest way to do this is by doing the following:
Press Windows + R to show the "run" dialogue box.
Type or copy/paste the following: %appdata%\StardewValley\Saves
Click "OK" to open the folder.

Step 2)
Open the folder with the name of your farm and then proceed to open the savefile that has the
name of your farm followed by a line of numbers with notepad.

Step 3)
Press ctrl+F and search for "QiChallenge" (without the quote marks) and hit search until you
see these three strings:
<questKey>QiChallenge#</questKey>
<questName>[QiChallenge#_Name]</questName>
<questDescription>[QiChallenge#_Text]</questDescription>

Step 4)
The # above stands for a random existent number that you will have to replace with number 9
on ALL of these. To clarify, the strings should look like this when you are done:
<questKey>QiChallenge9</questKey>
<questName>[QiChallenge9_Name]</questName>
<questDescription>[QiChallenge9_Text]</questDescription>

Step 5)
Save, start Stardew Valley and pay Mr Qi a visit. He should now offer the "Danger in the Deep quest"! No more annoying wait. I hope this helps ^.^ It sure helped me!