Kerberos authentication not working after IIS/SharePoint rebuild.

In the end, we ended up building an SSO Kerberos profile for each IIS application pool account with a static SPN to each. We then used an irule to route the request to the correct SSO Profile:

when HTTP_REQUEST {
    Parse URI to determine target Kerberos SSO Profile and store it in $ssoProfileName
    Ex: example.com/site2 -> $ssoProfileName = "example_site2" (example_site2’s spn would point to applicationPoolSite2Identity)
    WEBSSO::select $ssoProfileName
}

Thanks Kevin for all the help.