I understand that when you use the command advanced-balance ssl you got this error, Unable to connect to Site 0000PL, Request failed: 4 Send failed, SSL Handshaking failed (Error1705), but if you remove the command the application works.
Could you please try this?
content Secure_Content_443
protocol tcp
add service USPLSSCWW901_443
add service USPLSSCWW902_443
vip address 192.85.31.153
advanced-balance SSL
port 443 < ---- add this please
application SSL < ---- add this please
active
Please let me know if works.