Your plan should work fine--starter fertilizer 7 days in advance; why not?
Would you mind? Compare the results with starter fert at the same time as the seed.
And would you mind? Compare results using an ordinary turf fertilizer.
Paying top dollar for a starter fertilizer is fine...HOWEVER...if phosphorus levels in the soil are adequate---why add more? How much is enough? Which is more important--nitrogen or phosphorus?