Since my last comment here, I had the opportunity to work on integrating Stripe for a client's project.
I decided to take that experience and see if I can make it work with an Unbounce page.
Now a few days later, I'm happy to report that it's possible.
You can see a live demo right here.
For those interested, I've packaged the whole thing as a couple of scripts that you can purchase for your own projects.
P.S. The scripts use Stripe's embedded checkout form and it's only for one time purchases.
In theory, it can be made to support subscription payments but that opens up the question of what happens after you charge someone for a subscription. Usually, you'll need to update a database or a system but there are far too many of those to cover them with a general script.