Adding many Baumgartner clubs

I define a homogeneous \(\aleph _2\)–c.c. proper product forcing for adding many clubs of \(\omega _1\) with finite conditions. I use this forcing to build models of \(\mathfrak {b}(\omega _1)=\aleph _2\), together with \(\mathfrak {d}(\omega _1)\) and \(2^{\aleph _0}\) large and with very strong failures of club guessing at \(\omega _1\).