The shafts they come with are called the 3-1/2" shafts. It will work if you router out 1/4" of material below the control panel OR recess them from the top. I know SlikStik is doing your panel, so I don't know if they will accomodate that. You can also get 4" replacement handles, but you have to look for them.
One other option is to get the SlikStik stainless handles for the P360s. With a little modification they will work in the Wico bases (so I'm told).