Thanks to suggestions by Willeke (thanks so much for your help!), there is a solution. It involved subclassing NSView (I called it MyView), moving all of the tracking area handling into that view, and removing it from the ViewController. MyView.m is:

//
//  MyView.m
//  Repro
//

#import "MyView.h"

@implementation MyView
{
        NSTrackingArea  *trackingArea;
}

- (void)viewWillMoveToWindow:(NSWindow *)newWindow
{
        if (newWindow)
        {
                newWindow.styleMask |= NSWindowStyleMaskFullSizeContentView;

                [self setupTrackingArea:newWindow];
        }
        [super viewWillMoveToWindow:newWindow];
        return;
}
- (void)updateTrackingAreas
{
        [self setupTrackingArea:self.window];

        [super updateTrackingAreas];

        return;
}

- (void)setupTrackingArea:(NSWindow *)window
{
        if (trackingArea)
                [self removeTrackingArea:trackingArea];

        NSTrackingAreaOptions   options = NSTrackingMouseEnteredAndExited | NSTrackingActiveAlways;
        trackingArea = [[NSTrackingArea alloc]initWithRect:self.bounds
                                                   options:options
                                                     owner:self
                                                  userInfo:nil];
        [self addTrackingArea:trackingArea];
        return;
}
- (void)mouseEntered:(NSEvent *)event
{
        [self showTitleBar];
        [self showWindowButtons:self.window];

        return;
}
- (void)mouseExited:(NSEvent *)event
{
        [self hideTitleBar];
        [self hideWindowButtons:self.window];
        return;
}

- (void)showTitleBar
{
        self.window.titlebarAppearsTransparent = false;
        self.window.title = [NSProcessInfo processInfo].processName;
        return;
}
- (void)hideTitleBar
{
        self.window.titlebarAppearsTransparent = true;
        self.window.title = @"";
        return;
}

- (void)hideWindowButtons:(NSWindow *)window
{
        // hide the minimize and zoom buttons (yellow and green)
        [window standardWindowButton:NSWindowZoomButton].hidden = true;
        [window standardWindowButton:NSWindowMiniaturizeButton].hidden = true;
        [window standardWindowButton:NSWindowCloseButton].hidden = true;
        return;
}
- (void)showWindowButtons:(NSWindow *)window
{
        [window standardWindowButton:NSWindowZoomButton].hidden = false;
        [window standardWindowButton:NSWindowMiniaturizeButton].hidden = false;
        [window standardWindowButton:NSWindowCloseButton].hidden = false;
        return;
}
@end