I'm not sure I completely follow. What exactly is coming over when you clone a record? As I understand things the activity information in the Marketo frame on the layout shouldn't follow because it isn't even data in SFDC.
The last Interesting Moment carries over during the cloning.
You can use either Workflow Rules or APEX trigger on the SFDC side to reset these custom fileds to NULL when a new lead is created (cloning fire the same event) in SFDC.
In you rule critieria if you are using Workflow Rules, make sure that you use Field="Original Source Type" equals "salesforce.com" so that you don't reset these fields if the lead is created from Marketo or any other method. For example, a lead created from form fillout and a triggered campaign created some interesting moments. You don't want to NULL in this scenario.
This doesn't work unfortunately. It only works if the original Contact record's Original Source Type = salesforce.com because all values are copied into the new record. So if the original record's Original Source Type = Web Page Visit, for example, the workflow won't fire. So, it looks as though a workflow won't do it, so it might require an APEX trigger because of that limitation.