In my opinion, I don't think you have an argument in regards to the payment. If i am understanding, their top lease would have become effective 8/30/2011, after the previous lease expired. You cannot have two leases that are active and effective at the same time, so because they began "operations" within the primary term of your first lease, the renewal lease never came into effect. It makes sense that they should not pay you for something that you cannot give to them (ie...you cannot renew them your executive rights to lease, because you were still subject to your prior lease).
As some of you all have discussed, "operations" is a loose term in Oklahoma. There is no set definition. Simply clearing dirt around for a location is often considered "operations for drilling a well." So in that regard, it sounds like the lessee has met that standard. Do not be surprised by the fact that they "conveniently" began operations only a few days before your lease expired - many operators do this before a large group of leases are set to expire. You have to remember, the lessee probably has several hundred acres leased in your section, and a large chunk of that might have expired if they did not begin when they did. You can rest assured they did not choose their timeline in order to "screw" you as a mineral owner. It happens each and everyday.
The only other requirement for commencing operations is that the lessee work in good faith and with due diligence, without long periods of non-operations. A lessee does not have to be enganged in dirt work, concrete work, gravel, etc...each and every day. Weather, drilling schedule, and contractors sometimes will not allow that to happen. So as long as they continue with "due diligence"...whatever that means to you...and as long as a well is drilled within a reasonable time (this length is also debatable, however I've heard before that as long as a well is drilled within a few months, it likely can be considered they are acting with due diligence), then they are doing what is required of them.
The fact that they have been in operations since mid-August does not surprise me at all. As i've been informed before, it is common and accepted that a drilling location can sometimes take months.
Did the lessee not attempt to renew you before August? That seems a little late for them to be trying to get renewal leases. As i have learned with my own minerals, it's a gamble if you hold out for more money. Sometimes it's best to take a solid offer when it's presented, and not have to worry about situations like this.