Hello CDLTeacher,
Thanks for reaching out to the Apple Support Communities. We're glad you reached out. We can appreciate the hard work that you're putting in with the challenges of distance learning. From your message it appears that the QuickTime "Stop screen recording" button is not appearing in the menu bar, and you'd like to know if there is a keyboard shortcut.
This article provides the keyboard shortcuts and gestures that can be used in QuickTime: Keyboard shortcuts and gestures in QuickTime Player on Mac - Apple Support. When reviewing the list we didn't see one to stop the recording. You can leave feedback on the Apple site regarding adding this feature: Product Feedback - Apple.
With that being said there may be a couple of options which may help. The first is to make changes to the status menu icons that are showing in the menu bar. You can do this with the following steps from "Status menus" in the What’s in the menu bar on Mac? - Apple Support article:
"You can add status menus, such as the emoji viewer or a Volume control icon. You can also add status menus for some apps when you install them.
To rearrange the status menu icons, press and hold the Command key while dragging the items. To remove an icon, press and hold the Command key and drag the icon out of the menu bar."
You can also change how some of the information is shown in the menu bar. This can save some space allowing other icons to be shown. You can adjust how the date and time is shown. This can be done by going to System Preferences > Date & Time > Clock.
You can also remove your name from showing in the menu bar. To do this you can go to System Preferences > Users & Groups > unlock the padlock in the bottom of the left corner > select Login Options (at the bottom of the list of users) > You can then deselect "Show fast user switching menu" or change the way it's displayed. You can choose from Full Name, Account Name, or Icon.
All the best.