Thank you for clarifying.
You still do not add the income taxes form the $1475.56 to your basis. The effect of the transaction is that the company gave you extra salary for $1475.56 and you used it to buy those shares. That you have to pay tax on the extra salary does not change the price you paid for those "free" shares.
Think about it outside of the ESPP context.
If you earn $1000 from salary and use it to buy some stock shares in a regular brokerage account, your basis it $1000. That you also have to pay income and FICA tax on the $1000 is irrelevant. That is what is happening here.
Does that make sense?
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