You might try the following. It didn't delete my conversations on my LG G2. But if there's something you can't live without, forward it to your email or share it with some other application.
Settings | Application Manager, scroll to the right to All.
Scroll down to Messaging. Select it by pressing on it.
Clear Data. Clear Cache.
Power-cycle your phone (Power off and restart).
See if that helps.
If there was a way to perform a low-level cache wipe, I'd suggest that. But I don't think that's possible on our LGs.
Sure, try a replacement. And with the people I converse with often, I use Whatsapp, which is superior, because you can tell when the other party is online, when they are typing, when they've seen the message. While it's not an SMS app, you can send pictures and video, and it is available on iOS and Android.