sorry, i do not fully understand.
The live site is using version 3.7.0 of the theme and uses Visual Composer for the homepage. it has been like this since it was built and it uses Kuteshop Visual Composer elements so how can there be a problem with it using WPbakery when you made elements for it?
See the attached image
You also list wpbakery/visual composer as a feature of the theme
Features List:
Multi-Purpose Design
Plenty of Widgets
Multiple Page Styles
Social Sharing Features
SEO Optimized
Super Cache
Responsive Design
Unlimited Colors & Layouts
Unique Homepage Layouts: More Amazing Concepts Are Coming Soon!
Easy to Install Demo Data
Visual Composer: Page Builder for WordPress ($33 Value)
Revolution Slider ($18 Value)
Powerful Ajax Tab
Supported Multi-vendors plugins such as: Dokan, WC Multi-vendors, WC Marketplace, WCFM Marketplace
The Kuteshop Toolkit pluginnis very 1.5.4, do you have an updated version of this?
In version 4 of the theme did you basically make a new theme from scratch which would explain why it is not possible to upgrade from version 3 > 4?