In case it helps anyone else, I was able to get this working by leaning on this code to hold the view controller:
https://gist.github.com/timothycosta/a43dfe25f1d8a37c71341a1ebaf82213
struct ViewControllerHolder {
    weak var value: UIViewController?
    init(_ value: UIViewController?) {
        self.value = value
    }
}
struct ViewControllerKey: EnvironmentKey {
    static var defaultValue: ViewControllerHolder? { ViewControllerHolder(UIApplication.shared.windows.first?.rootViewController) }
}
extension EnvironmentValues {
    var viewController: ViewControllerHolder? {
        get { self[ViewControllerKey.self] }
        set { self[ViewControllerKey.self] = newValue }
    }
}
extension UIViewController {
    func present<Content: View>(
        presentationStyle: UIModalPresentationStyle = .automatic,
        transitionStyle _: UIModalTransitionStyle = .coverVertical,
        animated: Bool = true,
        completion: @escaping () -> Void = { /* nothing by default*/ },
        @ViewBuilder builder: () -> Content
    ) {
        let toPresent = UIHostingController(rootView: AnyView(EmptyView()))
        toPresent.modalPresentationStyle = presentationStyle
        toPresent.rootView = AnyView(
            builder()
                .environment(\.viewController, ViewControllerHolder(toPresent))
        )
        if presentationStyle == .overCurrentContext {
            toPresent.view.backgroundColor = .clear
        }
        present(toPresent, animated: animated, completion: completion)
    }
}
Coupled with a specialized view to handle common elements in the modal:
struct ModalContentView<Content>: View where Content: View {
    // Use this function to provide the content to display and to bring up the modal.
    // Currently only the 'formSheet' style has been tested but it should work with any
    // modal presentation style from UIKit.
    public static func present(_ content: Content, style: UIModalPresentationStyle = .formSheet) {
        let modal = ModalContentView(content: content)
        // Present ourselves
        modal.viewController?.present(presentationStyle: style) {
            modal.body
        }
    }
    // Grab the view controller out of the environment.
    @Environment(\.viewController) private var viewControllerHolder: ViewControllerHolder?
    private var viewController: UIViewController? {
        viewControllerHolder?.value
    }
    // The content to be displayed in the view.
    private var content: Content
    public var body: some View {
        VStack {
            /// Some specialized controls, like X button to close omitted...
            self.content
        }
    }
Finally, simply call:
ModalContentView.present( MyAwesomeView() )
to display MyAwesomeView inside of a .formSheet modal.