How about an app that just, well, sends the SMS texts to your email, as regular emails? A filtering rule would put them under a certain tag and skip inbox.
The upside of the design is that it requires only one, very clear, permission: send emails to a given address.
SMSBackup+ makes the sender the contact / phone number and the receiver as your number. It's been fantastic for archiving all of my texts and such. I've been able to search it all relatively easily.
The upside of the design is that it requires only one, very clear, permission: send emails to a given address.