There isn't anything that Vesper is doing that can't be done on the web. You could even write Vesper as a single-page app, and use a ServiceWorker with Firebase or PouchDB or whatever to run the sync. The infrastructure to do all this is very, very easy to do on the web.
This is not rocket science-- this is how far the web has come in a very short time. The UI could absolutely be the same as the iOS native app and while you might have a bit of scrolling hesitation on the interface, it would be perfectly accessible.
Suddenly you're on every mobile device, Android, iOS, iPad, desktop, whatever. The absolute hardest and most time-consuming endeavor would be to get the Stripe account set up for the one-time "in-app" payment to get sync working.
John and Brent and Dave made a fine app in 2012, but I would certainly hope that the next Vesper starts out life as a web app.