All you have to do is:
1. Find out how to get the weekday through sql
2. Add a table with the dungeon id's (thats more of a comfort change, although it also makes the procedures look less messy)
3. Perhaps squeeze the mandatory code into an additional procedure which is then called from (2) locations within both the single and party (?) dungeon clear set procedures
4. Add a counter for each dungeon, you can either extend the character table for it (make sure to allow NULLS or add "0" upon character creation, else creating characters won't work until thats fixed) or (i recommend that over the character table bit) - create an additional table solely for the run counters which gets the sum of all runs done per character (you can even get an account wide summary through both ways allowing to create some more advanced ways of rewarding your players)