I am currently working on a flow chart. The mwe (see below) produces the following output:

How can I achieve the following, desired output, ideally without having to declare additional coordinates/nodes? I want the Casting nodes to be connected to the horizontal line between Basic Oxygen Converter and Electric Arc Furnace through a vertical line. Also, how can I center the whole group of Casting nodes relative to the nodes Basic Oxygen Converter and Electric Arc Furnace?

mwe
\documentclass[margin=1cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usetikzlibrary{calc}
\begin{document}
\tikzset{%
every node/.style={rectangle,draw,inner ysep=3mm,text centered}
}
\begin{tikzpicture}[node distance=20mm and 10mm]
\node (boc) {Basic Oxygen Converter};
\node[right=of boc] (eaf) {Electric Arc Furnace};
\draw (boc) -- (eaf);
\node[below left=15mm and 10mm of $(boc) !.5! (eaf)$] (mediumslabcasting) {Medium Slab Casting};
\node[left=of mediumslabcasting] (thickslabcasting) {Thick Slab Casting};
\node[right=of mediumslabcasting] (bloomcasting) {Bloom Casting};
\node[right=of bloomcasting] (billetcasting) {Billet Casting};
\draw (mediumslabcasting) |- ($(boc) !.5! (eaf)$);
\draw (thickslabcasting) |- ($(boc) !.5! (eaf)$);
\draw (bloomcasting) |- ($(boc) !.5! (eaf)$);
\draw (billetcasting) |- ($(boc) !.5! (eaf)$);
\end{tikzpicture}
\end{document}

