I'm sad to hear about your text messaging issue that's still going on when you attach images in the message. Let's get into this a bit further. To begin, and so I don't assume, please provide the make and model of your device as well as the messaging app(s) this happens on. Also, aside from the slowness in attaching images, what other issues, if any, are you encountering (force closing, error messages, etc.)?
sullynole, the factory reset is typically the last troubleshooting step. We do not show any network issues causing the problem. Have you received any information from the manufacture?
Limiting yourself on sending photos isn't the most desirable solution, sullynote. Do you have any trouble sending pictures from your Gallery app? You mentioned a factory reset was done previously. Was all your information restored from a backup after the reset was completed?
Do you have Wi-Fi available to test on? If so, please connect to Wi-Fi and test sending an image. Is it as slow to load? This would at least allow a comparison to see if the images loading slowly is the cellular data signal, or something else.
This issue isn't tied to the mobile network. The slow load occurs in the Verizon and Samsung messaging apps themselves. Recent pictures take a long time or fail to load into the text message before actually sending the message out.