Regarding:
"An existing connection was forcibly closed by the remote host" or "The request was aborted: Could not create SSL/TLS secure channel."
This typically indicates either an issue with the the initial TLS handshake between your .NET server and the Apple Pay server, or the client authentication response (the two-way TLS) side of the handshake. To determine this, I would make your server side logs as verbose as possible and checkout which part of the handshake is being shut down by the remote.
As an aside; this is typically an issue with communication on the client authentication (two-way TLS) side. This can be due to your servers not using the Merchant Identity Certificates correctly, or having it be malformed.
Do Apple not have any working examples of successfully integrating with Apple Pay from an ASP.Net website?
Due to the vast amount of different server side combinations out there we have an example of the client side, via
Apple Pay on the Web Demo, and document
Requesting an Apple Pay Payment Session.Matt Eaton
DTS Engineering, CoreOS
meaton3@apple.com