Vertically Scroll PageView from SingleChildScrollView - flutter

Question

I have a tab bar with a PageView inside each TabBarView. Each PageView has a ListView and when I scroll it, how can I scroll from the Scaffold's SingleChildScrollView rather than just scrolling the ListView inside the TabBarView?
Currently, the tab bar stays on the same position when I scroll the TabBarView, which looks terrible. How can I scroll individual TabBarView from SingleChildScrollView?
I tried applying primary:false and NeverScrollablePhysics() to the ListView, but didn't turn out the way I wanted it to.
class MyApp extends StatefulWidget {
#override
_MyAppState createState() => _MyAppState();
}
class _MyAppState extends State<MyApp> with SingleTickerProviderStateMixin {
int currIndex = 0;
TabController _tabController;
#override
void initState() {
super.initState();
_tabController =
TabController(vsync: this, length: 3, initialIndex: currIndex);
_tabController.addListener(() {
_handleTabSelection();
});
}
void _handleTabSelection() {
setState(() {
currIndex = _tabController.index == null ? 0 : _tabController.index;
});
}
#override
Widget build(BuildContext context) {
return Scaffold(
body: SafeArea(
child: DefaultTabController(
length: 3,
initialIndex: 0,
child: SingleChildScrollView(
child: Container(
height: MediaQuery.of(context).size.height,
child: Column(
children: [
Container(
child: Column(
children: [
Padding(
padding: const EdgeInsets.all(8),
child: Container(
child: Text(
"HOME",
style: TextStyle(fontSize: 25),
)),
),
_buildTabBar(context),
],
),
),
Expanded(
child: _buildTabBarView(
context,
),
)
],
),
),
),
),
),
);
}
TabBarView _buildTabBarView(BuildContext context) {
return TabBarView(
controller: _tabController,
children: List.generate(
3,
(index) => Container(
color: Colors.red,
child: ListView.builder(
itemCount: 50,
itemBuilder: (context, index) {
return Padding(
padding: const EdgeInsets.all(8.0),
child: Container(
height: 60,
color: Colors.blue,
child: Center(child: Text("$index"))),
);
},
),
)));
}
Widget _buildTabBar(BuildContext context) {
return Padding(
padding: const EdgeInsets.only(left: 8.0, right: 8),
child: Container(
height: 45,
width: double.infinity,
decoration: buildTabBarStyle(),
child: TabBar(
controller: _tabController,
isScrollable: false,
tabs: List.generate(
3,
(index) => Center(
child: Text(
"$index",
style: TextStyle(color: Colors.black),
),
)),
),
),
);
}
BoxDecoration buildTabBarStyle() {
return BoxDecoration(
color: Color.fromARGB(255, 230, 248, 255),
border: Border.all(
width: 1,
color: Colors.black,
),
borderRadius: BorderRadius.all(Radius.circular(10)),
);
}
}