Replace Messages app with something else and have it use my phone number?
According to a third party wanting the same, Apple doesn't allow this: https://support.signal.org/hc/en-us/articles/360007321171-Can-I-send-SMS-MMS-with-Signal-

There was once an app which synced your sms and allowed sending and receiving through an app: mysms. It would still work if you put the sim card into an android phone, but that doesn't seem to be what you want, as you'd now need another phone number for calls on your iphone...

The closest you can get on an iphone is probably through your provider's sms website offerings, like this one: https://n.vodafone.ie/business/products-and-solutions/mobile-communications/bulk-texts.html

Depending on your provider, you could probably put a shortcut somewhere on the iphone which opens a page where you can see your sms inbox and write new ones - with some business features on top.

Then you just need to deregister your phone number from imessage and make it work with your email address only. Anyone entering your phone number on imessage should then get to send the message in green.