But then I went to the company's licensing page and things got murky really fast. It turns out that the ExtJS won't allow you to use Ext under its LGPL (3.0) license "[i]f you plan to distribute Ext in a product that will be packaged or sold as a software development library, toolkit or plug-in-based framework."
It's a bit like saying, "You can use this as open source so long as you use the software how we'd like you to use it. If you have any money, forget open source: pay us instead."
So how is this open source? This is a wholesale rejection of the Open Source Definition (#6). It's fine if ExtJS wants to distribute its software under a proprietary license, as it does today. But it's not fine for it to claim to be open source but then to constrain the use of its code in such a way that clearly makes it closed-source software.
Choose, ExtJS. Your current licensing model is not open source.