Well - the issue is with your rules, I think.
The field /my:Liaison_Time/my:Liaison_Total_Daily_Regular_Time_For_Billing is being set based on the idea that the form will only have a single, 8 hour day. When you merge the forms, you have multiple days.
Same with this field: /my:Liaison_Time/my:Liaison_Total_Daily_Overtime_For_Billing
But I wonder - I guess, the expectation of merging behavior would be that these fields would just be added, right? Not that the rules would fire again....
So I think what you are saying is that the merge behavior is not working as you'd anticipate.
You could test this, I think. Add a condition to the rules so that you can control whether they fire (like "FieldA = true" then put a control bound to that field on your form so you can toggle it). And then try merging in a scenario where the rules won't fire - see if the fields are added instead of the rules firing....
I guess it seems like your rule conditions may need to be the distinct number of dates * 8 to determine whether there is overtime or not - does that make sense?