MakerBot Print is our newest print-prepration software, which supports native CAD files and STL assemblies,
allows you to interact with all your printers via the Cloud, and many other exciting new features.
Yup, the Thingiverse Customizer has been broken since about December or so. I understand that Thingiverse is busy working on fixing it. So hopefully we'll have it back at some point soon.
Nope, no other apps like Thingiverse Customizer, that I know of. However, the best way to work with parametric SCAD models, is actually directly in OpenSCAD on your local machine anyway. If an SCAD model has been written to integrate with the Thingiverse Customizer, then you should see all the user configurable parameters at the beginning of the file, formatted as the Thingiverse Customizer requires.
I try to comment my code as descriptively as possible, to make it easier for people to use my SCAD models, even if they don't know much about coding. In all of my parametric SCAD models, I structure the code in the same way. If you start at the top of the file and scroll down, the first code section will be a bunch of constants, which you'll want to just leave as they are. And then the second code segment from the top, commented as "Thingiverse Parameters", are all the public parameters that you would normally see in the Thingiverse Customizer. You can just adjust those public values in that second section directly, and press F5 to update the model in the 3D view. Once you get used to doing that, there is a good chance you may end up actually preferring to work with SCAD models in OpenSCAD.