It would be great to write Macros that open the group finder Frame and init a search.
I managed to open the frame by

/run if not GroupFinderFrame:IsVisible() then PVEFrame_ShowFrame("GroupFinderFrame") end
/click GroupFinderFrameGroupButton4
/run LFGListCategorySelection_SelectCategory(LFGListFrame.CategorySelection,2,0)
/run LFGListCategorySelectionFindGroupButton_OnClick(LFGListFrame.CategorySelection.FindGroupButton)

But PGF filter fails. I have to manually activate/deactivate it in order to filter properly.
It would be great if you could add an option for this to save some clicks

Should be fixed in one of the last alpha versions. Check out e.g. 1.10-5-g67bc4d4-alpha.

works fine