Hello iPhoneUser976,
From your post we can see that you need to get screenshots of older messages that include the date and time.
You're right, this does seem to be the best way to capture what you need. If the messages are on the same day but take up your screen, you might need to overlap some to show they belong in the thread.
You also might find a solution for your need in the App Store. When you're searching to pick the best app for this, make sure to check the ratings and reviews to see if it fits your needs.
We hope this helps.