After piecing together a lot of different resources by diligent hunting about on Google, I've discovered you can actually launch a WebApp from a SpreadsheetApp custom menu, and it's not that hard at all.
All you do it deploy the WebApp as normal, and use the script's 'Project properties' File menu option to retrieve the 'Project key'. This you simply copy/paste into your client SpreadsheetApp's 'Find a library' box as described here
Once the library is installed, you can add a custom menu to invoke the Library's doGet() & return the app object to show in your client SpreadsheetApp:
function Shoo() {
var app = FooManShoo.doGet();
SpreadsheetApp.getActiveSpreadsheet().show(app);
}
function onOpen() {
var entries = [{name : 'man', functionName : 'Shoo'}];
SpreadsheetApp.getActiveSpreadsheet().addMenu('foo', entries);
}
Hope this helps someone else! :)