Is there any way to put a segmented picker into a scrollview in SwiftUI?

I have the following code. It only really works if I tap and drag right below or at the bottom of the segmented picker. I need to try tapping and dragging multiple times before I hit the right spot and it works, which is a terrible user experience. I can switch it to a wheel picker, but it just doesn't look as good. Any suggestions? (Changing from a VStack to HStack doesn't really do anything. I also tried putting the scrollview in different spots in the hierarchy. I want a scrollview because there might be a lot of items in the picker, and the segmented picker doesn't look good with 6+ items, so I want the scroll effect.)

ScrollView(.horizontal) {
    VStack {
        Picker(selection: $discoverServices.myShowIndex, label: Text("Select Show")) {
            ForEach(0..<myShows.count) { i in
                Text("\(self.myShows[i].name!)")
            }
        }.pickerStyle(SegmentedPickerStyle())
    }
}