As I can see you are using the following too: http://stylebuilder.telerik.com/
which is already old and is not supported.
I will suggest to use the following: http://themebuilder.telerik.com/
which is based only to our LightWeight rendering and uses SASS variables to create a new skin.
It is also well supported and soon we will update it again with R3 service pack 1 DLLs. Right now it runs Telerik.Web.UI version 2016.3.914.
It is much more powerful and well built compared to the old tool. It also allows you with just a few clicks to create the whole controls bundle as it works directly with the variables that build all controls instead of browsing control by control in order to make all changes. It also contains the Bootstrap skin as an option to use it as a base.
Note that lightweight does not contain images/sprites but CSS gradients and font icons, so you will not fall into the web resource problem.
Here is a help resource: http://docs.telerik.com/devtools/aspnet-ajax/theme-builder/overview that will guide you through the skin creating process.
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