How to export a single WhatsApp chat?
Requirement: rooted device. 

Download WA Tweaks and install it. 
Close WhatsApp process, open WA Tweaks inside the WATweaks App and there you would find a "Conversation" tab. Load conversation.  As your chat sizes are huge it may take alot of time. From there you can get complete conversation backed up / emailed.

You can see demo video of the app here on my channel. 
This should solve your issue. If you have a low end phone it will get stuck.