I have stitched something together after a fair amount of head scratching.

1. First, there is live_render, which allows instantiating a live view inside a functional component.

   <%= live_render(@conn, MyApp.ToolAccessModalDialogLive %>

   (Not really sure why the syntax is <%= ... %> rather than a usual component instantiation.)

2. Now that I have a live view to send events to, I can use JS.push(...) However, I need to specify the target: JS.push(... target: ...) because the button that triggers showing of the modal dialog is outside that dialog.

3. Using target: "modal-access" (see the snippet in my original question) does not work because "modal-access" is the id of the modal dialog, the actual live-view is nested inside.

4. I specified the id in <%= live_render(@conn, .., id: ...) but that does not work either because the id gets overwritten with the auto-generated one.

5. In the end I created a dummy <div id="receiver"> inside the live view and now I can JS.push events to that div. That works!

6. The last problem was getting rid of the layout injected to the live_render-ed element. I ended up creating a new helper in MyAppWeb and then in my module I replaced

use MyAppWeb, :live_view

with

use MyAppWeb, :live_render

where live_render is like live_view but without the layout:

  def live_render do
    quote do
      use Phoenix.LiveView,
        layout: false

      unquote(html_helpers())
    end
  end

K.