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Why not just use Sendgrid or similar for SMTP emails to customers, get a dedicated IP with them and have way less concern.

I always prefer to isolate those things from the main corporate email and reputation anyway.

You don't want your main domain getting hacked and affecting customer emails or vice versa.

Have you spoken to an account manager there? I send way more than that on a regular basis. I do it sequentially for simplicity, I wonder if that makes a difference.

You should be using a dedicated transactional email provider, and accept the additional cost. At most scales, this is the correct business decision.