O.K. I finally got to the bottom of this.
It turned out to be a reverse DNS issue at the server hosting provider that resulted in a reverse DNS query timeout. This only showed up on HTTPS connections from the Kindle Fire and Nook Tablet, because there is an Android 2.3.x bug, that causes the client to unnecessarily perform a reverse-DNS query on https negotiation:
http://code.google.com/p/android/issues/detail?id=13117
There is a workaround in the details (follow the link above) to keep clients from performing the unnecessary rDNS query. My guess is that the native web browsers on Android 2.3.x implemented the workaround (which is why the connection from the web browser on the Nook Tablet and Kindle Fire is fast), but that the network.request() implementation in Corona does not implement the workaround to avoid the unnecessary reverse-DNS query.
The network.request() implementation should really be updated to implement the workaround to avoid an unnecessary rDNS query if the target OS is an Android platform affected by this bug.
Note: The server rDNS issue was verified using:
dig -x serverIP +trace
[import]uid: 14461 topic_id: 36061 reply_id: 143626[/import]