APMR, the more I read your posts the more I think you are just winding us up.
For instance read this again.
If a pilot on a tour away from home base is not required for duty on any rostered duty day, such a day shall be considered a day free of duty for rostering purposes but not a designated day off at home base.
Go away for 10 days, your "day off" is not a day off but a day free of duty.
A designated day off is only relevant at home base.
A penalty payment is only payable for working on a designated day off.
Therefore working on a day free of duty whilst away from home base gets you no penalty payment.
I cannot make it any simpler than that and I must say that if you cannot follow the implications from this then it must be a windup.
And if I cannot get you to understand this simple clause and it's implications why even bother with the rest of your dribble.
Called Lawrie yet have you? Spoken to your rep yet? Probably not.
And maybe you are not a pilot at all???
OAH