W6100 with lwIP or other 3rd-party software stack

The io6Library seems to provide a good foundation for a socket-level interface to TCP and UDP, but the higher level examples found on WIZnet ioLibrary & io6Library examples · GitHub seem more for demonstration purposes rather than development due to lack of updates and documentation. Are there any examples, resources, or suggestions for integrating 3rd-party software stacks to support TLS, HTTP, ICMPv6, MQTT, with the W6100?

You should find many libraries on the WWW which handle “what ever” protocol and which are independent of PHY.
Then you just need to write wrapper functions, which connect your PHY library to a e.g. HTTP library.