xmobar does not appear on top of window stack when xmonad starts

Two months later I figured it out. The problem is that statusBar does not register the events of Hooks.manageDocks properly. Once xmonad is running all works well because manageDocks is able to update the Struts on every window event. But in the moment that xmonad is starting the event of making the first windows fullscreen happens before the events from manageDocks. This mages that first open window to ignore the existence of xmobar.

manageDocks has its event handler that must be set as the last event handler, therefore statusBar cannot be used. Instead, it is necessary to make xmonad call and configure xmobar manually through dynamicLog, manageHook, layoutHook and handleEventHook. A minimalistic configuration for this would be:

main = do
    xmproc <- spawnPipe "xmobar"
    xmonad $ defaultConfig
      { modMask            = mod4Mask
      , manageHook         = manageDocks <+> manageHook defaultConfig
      , layoutHook         = avoidStruts  $ layoutHook defaultConfig
      -- this must be in this order, docksEventHook must be last
      , handleEventHook    = handleEventHook defaultConfig <+> docksEventHook
      , logHook            = dynamicLogWithPP xmobarPP
          { ppOutput          = hPutStrLn xmproc
          , ppTitle           = xmobarColor "darkgreen"  "" . shorten 20
          , ppHiddenNoWindows = xmobarColor "grey" ""
          }
      , startupHook        = setWMName "LG3D"
      } `additionalKeys`
      [ ((mod4Mask, xK_b), sendMessage ToggleStruts) ]

This makes all events to be processed by docsEventHook and ensures that layout changes made by docsEventHook are the last ones applied. Now

lowerOnStart = False

(or True) works as expected in all cases within xmobarrc.

Comparing your config, to my simpler one, which does work correctly in this regard, I see one difference that might do something:

from all the general behaviour options you have I only have

lowerOnStart = True

and not a single of hideOnStart, overrideRedirect etc.

The way you add xmobar in xmonad.hs is, as far as I can read, the same as mine.

In this case I'd try with as much default settings as possible, e.g. rename .xmobarrc so it's not picked up, and change xmonad.hs to e.g.

main = xmonad =<< statusBar "xmobar" xmobarPP toggleStrutsKey defaultConfig
toggleStrutsKey XConfig { XMonad.modMask = modMask } = (modMask, xK_b)

and see if it works. Later add bit by bit, and see when it breaks.