Great detective work.
I
suspect part of the issue is the ability of your school's network to support a lot of projects. Your detective works seems to support this theory This slow loading is not only an issue of your classes but perhaps the entire school. If others are running word processors, spread sheets, streaming audio or video inside or outside of classes and used by administrative staff...all these compete with your classes. App Inventor is not just a Web link...it is a Web application. You might check with your school's IT people. They may have a way to establish whether the school's Internet connection is near capacity (slowing some activities). What you described happens on under-powered networks. Is it the only issue? Probably not.
There are more things you all can try to get better performance:
1) Instead of using the Companion as it is, check the Use Legacy Connection . .MIT is experimenting with ways to optimize the live development environment. Checking the box allows a developer to make a connection similar to the way connections used to be made. Sometimes checking that box makes a difference in the way Companion performs. You guys might try that and hope there is an improvement.
2) I hate to say it (don't use Chromebooks...there is a reason Chromebooks are less expensive than regular PCs). There, I said it realizing you can't really do anything about it.
Since last year, loading projects for most users seems to take a while longer than it did a year ago for everyone, not just your students..
In your I have a dream Project, are the students providing supplemental material? If so, you could try running the basic project aia and loading and running that as a comparison The basic files are here
http://ai2.appinventor.mit.edu/?galleryId=5753789846913024 , unfortunately this is just a template having the basic images/sound files preloaded without the connecting code Blocks.
If the students are doing clever things (like adding their own resources) the Project can get huge. Test that by exporting the Project aia's of the students and checking file size. If an aia is approaching 10 Mb, that in itself is an issue (Projects with aia's greater then about 10mb will NOT generally load rapidly or in some cases, even compile). Large images and sound clips take a while to load.
Let us know how your school day goes and what you discover. Wish all of you success. If size is another part of the puzzle, someone here can perhaps help your students how to provided 'skinnier ' resources. A frequent culprit is using images with pixel dimensions significantly larger than about 300 x 480 pixels or so ... existing images can be reduced using an image manipulation program (Paint on Windows). I don't know what Chromebooks use.
--Steve