Wow. "It IS possible using an Android app, I have the screenshot. You said "The app just does not get an IP on a chromebook." but it does not provide the IP connection." Sad but true.
Chromebooks are cheap but in your case a false economy.
Will doing what you want to do ever be possible Evan? Someone from MIT will comment, your posts have been flagged. Give them a few days to reply.
There are many ways to get what a school needs. Ask the parents for donations of used Android devices no longer in use. Many or most phones that used to work with a paid subscription will work with WIFI as a development device . Just make sure the Contacts and personal information are scrubbed. Students will be very happy. Students can also share projects/devices .. many schools do that. There are other low cost options.
Be careful, you might get what you ask for... Sharing the Chromebook screen with both the Designer AND a live app? running side by side will provide a cluttered work environment. But, if that is what you hope for, good luck. It might be possible but not at the present.