Looks like they offer paid support, and the console branches obviously aren't public so you'd have to make a deal to access those.

No. Wrong. Console branches are available for free if you are approved by the vendor.

It's also being funded by a number of corporate sponsors. As I understand it, a studio or publisher will fund the development of a specific feature, while general development is mostly just spare time and donations.

No, Defold is developed by six full time and two part time developers. All developers are fairly compensated. Most of the work done on the engine is "general development" funded by corporate partners, studios and publishers. There is quite a bit of overlap between the needs of specific partners and the general development roadmap.