Split tunnel ACL should be standard ACL. Base on your post, I am under the impression that split tunnel ACL is extended ACL, but pls ignore if it's standard ACL.
Any chance you can post the config of the ASA? Base on the output provided so far, config seems to be OK, and seems like ASA is getting the ICMP echo and echo reply. Would be interested to see if it's actually being forwarded out the VPN tunnel.
Apart from ping, can you try TCP based application and see how it goes?