really there is not a whole lot to be confused about. Like I said earlier and this is something I deal with almost daily so trust me. You have to modify your address on your drivers license with in so many days of you moving. The same goes for the SDA.
I'm sorry but this is simply not true. With an Oklahoma drivers license, you have to go to a tag agency and modify your address in the DMV computer system but you do not have to get a new license. The same with the Oklahoma Handgun License, you have to notify OSBI of the new address, but you do not have to get a new handgun license.
Now when you are in the process of moving then no you dont have to change anything because you still are technically residing in Kansas. For this reason you can stay at your new residence for the purpose of moving personal possesions in to your home. If you still claim residency (Which is defined by where you spend the majority of your time) in Kansas but are staying a week to move things in to your home then you would not be a resident of Oklahoma so your Kansas I.D. would cover you.
If you are stopped and they ask why you are living in Oklahoma with an out of state I.D. then all you would need to explain is you are still in the process of moving to Oklahoma your just unpacking belongings and so forth. You really dont have to worry about a trooper asking you to prove it by following you home.
This is not an uncommon situation because people live in Oklahoma and own beach houses in Florida. Does it mean they need to change their I.D. over when they spend a week in Florida?
Your Kansas card is honored in Oklahoma so you should have no issues. Like I said earlier just lay low until you get around to getting your SDA. it takes about 3 months to get it so just "Visit" Oklahoma for a while ;-)
No need to "lay low until you get your OK SDA" either. OK honors the KS permit, doesn't matter what state your drivers license is from. As long as your KS permit is valid in KS then you are good in OK. You would have to check your KS laws to see if/when the KS permit becomes invalid, such as possibly getting a drivers license from another state. As soon as you establish residency in OK, you can take the class and apply for an OK permit.
After you finish moving, all you will need to do is get an OK drivers license, this will still cover your KS permit (as long as it remains valid in KS). Like I said, KS may not honor the permit once you change your residency status, you would need to check with KS on that.