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You are looking for a simple VGA switch. For example: http://www.amazon.com/MT-VIKI-VGA-Splitter-Amplifier-MT-15-2AV/dp/B00DRGDDX0/ref=sr_1_7?s=electronics&ie=UTF8&qid=1407127908&sr=1-7&keywords=2-port+vga+switch
Did you try using the -compression_level flag? It takes an int from 0-100 afaik (maybe the range is even higher, the docs just say "int"). That should set a lossy compression strength. There is also an interesting blog post about creating DCI compilant JPEG2000 encodes with FFMPEG for DCP's. Which require lossy encoded JPEG2000.
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