I discovered an alternative way to save the texts. A lot faster than individual screen shots, though not as pretty.
Instead of long-pressing the name, open a message and hit the menu button. Tap on Save messages, and then tap the check boxes. You can "Select all" however, due to the length of what I'm trying to save, all the messages won't be saved into a single file. So I did it in several steps, selected 5-6 messages, saved them and gave each a unique identifying name, for example: subject_1, subject_2, etc.
If someone knows of a more elegant way to accomplish this, I'd like to know. However, for now, this works for me.
Thanks everyone for you input.