WSUS Hangs on "Unused updates and update revisions"

Question

In our environment we have not cleaned up WSUS updates in a while, probably about a year. I have been tasked with cleaning it up and optimizing it. When I attempt to run the WSUS Server Cleanup Wizard, it hangs on "Unused updates and update revisions"
and doesn't do anything. The wizard then disappears and I am taken back to the WSUS Console where I see the following:
Error: Database Error
When I click copy error to clipboard, this is what is copied:
The WSUS administration console was unable to connect to the WSUS Server Database.
Verify that SQL server is running on the WSUS Server. If the problem persists, try restarting SQL.
System.Data.SqlClient.SqlException -- Timeout expired. The timeout period elapsed prior to completion of the operation or the server is not responding.
Source
.Net SqlClient Data Provider
Stack Trace:
at System.Windows.Forms.Control.MarshaledInvoke(Control caller, Delegate method, Object[] args, Boolean synchronous)
at System.Windows.Forms.Control.Invoke(Delegate method, Object[] args)
at Microsoft.UpdateServices.UI.SnapIn.Wizards.ServerCleanup.ServerCleanupWizard.OnCleanupComplete(Object sender, PerformCleanupCompletedEventArgs e)
In my research, I have found several solutions, and have tried a few of my own. Below I will list the ones I have tried: 
1. Run each item individually. IE, run superseded updates, then run expired updates after that finishes, then run unneeded update files after that finishes, etc. This did not work
2. Stop the WSUS IIS service and run "wsusutil.exe removeunneededupdates" this also did not work
The solutions I have found, but am hesitant to try (due to the fact that we are in a live production environment) are the following:
1. Re-Index the WSUS Database according to the following link: 
https://technet.microsoft.com/en-us/library/dd939795(v=ws.10).aspx
2. Deleting the files in the WSUS folder and running "wsusutil.exe reset" from the following link: 
http://windowsitpro.com/windows/quick-tip-resetting-wsus-server
I would like to know what, if any, impact either of these solutions will have on our environment, and which one would be the preferred method. I feel like I should use the first one, and if I still don't have any luck then try the second. My only concern
with the second method is that it might break something (not sure what, except updates). 
A little about our environment - 8,000 computers, WSUS and SCCM are on the same Server 2008 R2 server, we only have the one WSUS and SCCM server, so nothing downstream as far as WSUS is concerned. 
Thanks everyone!

Answer 1

UPDATE:
I have started going through and declining updates, and then going through SCCM and removing any expired updates from the SCCM side as well. I am now down to 3822 unapproved updates in WSUS, with a total of 13304 updates.
At this point I am STILL UNABLE to run the cleanup wizard to clean up any of these. It still hangs when it runs, and only on Unused Updates and update revisions. I have even tried running powershell scripts and command line utilities to clean WSUS up, and
still just hangs. I am pretty much at a loss, so any other advice would be appreciated.
One more question, should it resort to this: What impact does resetting WSUS have on a live environment, with 7000 plus computers? Should I have to resort to it, is this something that is going to cause any major issues? 
We do plan on preventing this in the future by running the database defrag once a month, and running the WSUS Server Cleanup Wizard once per quarter, but getting there sure is proving to be quite the challenge.
Thanks again!