-H in gcc mode doesn't print -include headers, but they are included in depfiles written by MMD and friends. Since /showIncludes is what's used instead of depfiles, printing /FI there seems important (and matches cl.exe).
There's more work to do for the interaction of /FI, /showIncludes, and PCH flags, but this is a strict improvement over what we have today.
Instead of giving HeaderIncludeGen more options, just switch on ShowAllHeaders in clang-cl mode and let clang::InitializePreprocessor() not put -include flags in the <command line> block. This changes the behavior of -E slightly, and it removes the <command line> flag from the output triggered by setting the obscure CC_PRINT_HEADERS=1 env var to true while running clang. Both of these seem ok to change.