I think you have a misunderstanding about what it means to establish domicile. It is not necessarily something that you choose, like checking a box on an application.
If you are living and working full-time in your new state, then you are a resident of that state. I suppose an exception would be if you were a student who was also working full-time, but that isn't the scenario you described.
States can have different rules about domicile for the average citizen and for those applying to one of its in-state schools. Sometimes those rules are the same. Sometimes the rules for the applicant are more stringent than those for others. However, it sounds like you've already confirmed with your new state's schools that you are in-state in their eyes.
At this point, it could be illegal for you to indicate to your old state's school that you are in-state applicant, because - from what you've described - you're not. It's entirely possible that your old state's school doesn't have the wherewithal to realize that. However, if you were to apply, be accepted, and attend school in your old state, then you are taking a risk (perhaps a small one) that they will (eventually) deem you an out-of-state applicant and force you to pay out-of-state tuition. They could even seek reimbursement for the difference between in- and out-of-state tution paid in years prior to the discovery of your domicile at the time of acceptance.