Do you have a better idea to reduce the amount of spam?

It's a good thing that it's very hard to send lots of mails to strangers

Spammers do everything you do and a lot more, yet most of them are blocked(and just imagine what would happen if they could send as many mails as they want without going through all those hoops, we'd get basically nothing but spam)

The only reasonable solution if you're not a big/reputable business is to use a service like mailgun/mailjet/mailchimp/sendgrid, for a small business it would cost next to nothing(or even just 0$, if you can get some free credits or a small free plan)

It will save you a lot of headaches