LTM SSL Offloading

If I may add, your capture is basically 6 different attempts to start an SSL handshake, starting with TLS1.2 and moving to TLS1.0. The odd thing is that the client's CLIENTHELLO message is met with an immediate failure by the server. This would usually indicate some egregious disparity between the client and server's capabilities. So quick questions then:

1. Are you doing anything specific in the client SSL profile?
2. Specific cipher selection?
3. Any non-default settings?
4. If you have made changes, what happens if you use a basic unmodified client SSL profile (except for the server cert and key)?

And in case there's something missing from the logs, do you see any server side traffic with a tcpdump?

tcpdump -lnni 0.0 port 80 and host y.y.y.y

where y.y.y.y is the IP address of the web server.