As to why the right hand box is so large, I believe it is because Beamer cannot tell how much vertical space is required. The overprint environments seem to throw off its space calculation.
One way around this is to make the right hand block a minipage with an explicitly declared height (75% of slide height seems to work for your example) and put the overprints inside the minipage. Your test file, suitably modified, is attached below. As a side note, I had to put a hard space to the right of the table; otherwise the hfill on that side was ignored. Paul #LyX 2.0 created this file. 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\end_index \secnumdepth 2 \tocdepth 2 \paragraph_separation indent \paragraph_indentation default \quotes_language english \papercolumns 1 \papersides 1 \paperpagestyle default \tracking_changes false \output_changes false \html_math_output 0 \html_css_as_file 0 \html_be_strict false \end_header \begin_body \begin_layout Title Title As It Is In the Proceedings \end_layout \begin_layout Subtitle Include Only If Paper Has a Subtitle \end_layout \begin_layout Author F. \begin_inset space ~ \end_inset Author \begin_inset Flex InstituteMark status open \begin_layout Plain Layout 1 \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash and \end_layout \end_inset S. \begin_inset space ~ \end_inset Another \begin_inset Flex InstituteMark status collapsed \begin_layout Plain Layout 2 \end_layout \end_inset \end_layout \begin_layout Institute \begin_inset Flex InstituteMark status collapsed \begin_layout Plain Layout 1 \end_layout \end_inset Department of 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