I'm Doug, and I'm very sorry to hear of your concerns. My goal is to provide you with excellent service today.
The fact that you received a note from the Principal indicating that they are still in the process of vetting you is a very good sign. They thus far have no reason to believe that they will not hire you and so you were told that the vetting process is still ongoing.
The facts you have relayed suggest that they feel you will be as great an asset to their school as you feel the desire to be part of the school program---and aside from the vetting process taking a bit longer than you are comfortable with---I see absolutely no red flags here and everything appears to be going well. It is just a matter of time until your hiring is confirmed and you are offered a contract.
Right now, when they are partway through your vetting, and your present supervisor gave you a glowing recommendation, everything looks great for you to have a new position in the immediate future. The chances look excellent.
You may reply back to me again if you have additional questions, and I will continue to assist you.
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I wish you and yours well in 2017,