That will always be a risk if you are borderline for DTI or credit score. Qualifying once doesn't guarantee you will qualify again on a re-pull. The car will be on the truck for a couple days at least, which should give you time to shop the rate if Alliant doesn't give you their top tier and you want to see if you can do better. Hard pulls all around the same time are grouped together and count as one.
What would be even worse than not qualifying 6 days before the car shows up is qualifying 31 days before the car shows up, and then when they re-pull your credit not re-qualifying (maybe even because of the first hard pull, although I'm not sure if that could really happen). I would call up Alliant and see what they say.
If you're concerned about the timing you could wait until it goes into production so you have the extra week, you just run the small risk that Tesla takes longer than average to build and then decides to ship by train.