"Also, even supposing downloading from your website is the only alternative you give me, to do that securely, you'll have to use HTTPS, you'll have to sign your binaries with a public key I trust, you'll have to provide signed hashes so I can verify the download, etc.--in other words, all the stuff you'd have to do if you maintained a third-party PPA."

This is how most professional Windows desktop software is distributed today. Also, you don't need a signed hash if the binaries are code-signed - you can verify that they haven't been tampered with by simply right-clicking on the binary and looking at the cert/SHA-1/SHA-2 signatures.