What is the easiest/quickest/most-pain-free way of turning my Windows desktop app into a web app? Looks like I might have to create a new web app and do a lot of copying. Is there a better way?
Not really
The other thing to be aware of is that some things that make sense in a desktop app may not work well in a web app
responding to keystrokes is one
By the time the web app is notified that such an event has happened - its already happened on the browser and you’re being told “hey this happened” unlike in a desktop app where its more like “hey this is HAPPENING right now !” and your code can react and to that keystroke rapidly
So some rethinking is in order when you move to a web app
That said IF you can hold off Xojo is supposed to be coming out with their entirely new Web 2.0 REALLY soon (I hope) and so if you start right now you’ll be writing a Web 1.0 app which will be superseded real soon now (fingers crossed)
@Norman Palardy What is the technical value of “real soon now?” 
well lets say if you told your friend you would be over “real soon now” and then showed up next year they’d be a bit put out
sooner than that 
Yes, you need to maintain a duplicate window and controls for desktop and web apps, but you can place any major code snippets in external classes and methods that are shared by both, so you only need to maintain one code base.
It is a bit painful, but certainly possible, and soon to become much easier with Web 2.0. I did an XDC 2020 talk on how to do this.