I've stumbled upon a variation to this solution that I find preferable, though I'll admit I don't entirely understand why it works.
First, let me clarify that I've also had problems with the debugger display area -- not just that the variable list ties up screen space, but also that the variable listing becomes "squashed" and unreadable when it gets overpopulated (instead of expanding into a scrollable list.) Ideally, I'd like a fix for that problem.
Thinking that the overflow setting might affect the scroll bar, I tried a few options, and noticed that the following CSS seems to remove the variable watch list and free up screen space, but leaves the debug view toggle button visible so the test mode remains usable.
tw-debugger {
overflow: hidden;
}