Hi L.Sheaffer,
I suggest that you instead cancel your current Method account and start a new one. I believe that once you purge your data from QBO, this will create several conflicts in Method, as it will no longer be able to locate data that it expects to find. This will also fail to remove any Method only data, such as the activities you have created.
I don’t believe Method will push any missing data back into QBO, but just to be safe, I recommend using the following order:
1) Cancel your current Method account. You can do this from your Subscription Portal located under Customize > My Account.
2) Purge your QBO data.
3) Sign up for and connect to a new Method account.
If you follow these directions, you should not have any issues purging your QBO data.
I hope this helps.
-Audisho