Hmm.... I assumed when you gave instructions to the OP for a PC you were speaking of a windows PC. I am afraid to sign out of iCloud on my PC though. It sounds like from your above message, you do not know how iCloud works on windows and therefore your prior message to the OP that "you shouldn't lose anything..." would not pertain to a windows PC.
Sorry that I assumed you were speaking of a windows PC. I have done all of your other steps besides signing out on the windows PC because firstly, I do not know how to and secondly I am afraid of losing data.
Can you refer me to someone who does know or is familiar with windows PC and iCloud as this issue is really out of control. I currently have 46 reminders that just went off when the last reminder went off on my iPhone. Those 46 are only persisting on the PC and on iPad as when I mark as completed on the phone they are gone as they should be.
I should also note, or re-note, that when I follow your first step of logging into iCloud.com to see if the items are there, I get a strange message that says can't load reminders It says "Reminders is taking longer to load than expected". When I try to click on a different application on icloud.com, like calendar, it loads instantly. Only reminders is doing this strange behavior on icloud.com. FYI....I have a super fast internet connection that is very stable so I know this problem is not on my end. I don't know if this is related to my problem but just thought I should give you all of the facts pertinent.
Thus, I kindly ask if this can be referred to someone who has windows knowledge because I have used iCloud on windows for as long as iCloud for windows has been available and I have never had this issue until a couple of weeks ago when some change was made to iCloud to fix a different problem that I believe in turn created my problem. This supposed fix to an iCloud issue, which I believe caused my issue occured around the 1st of August. I do not know the exact date but I do know that there was a system status entry on apple system status page on the day in question that said that iCloud had been down and had been fixed.