I also have the media-street system on my Epson R800. It also clogs quite regulary. What I found is, that when it sits for a while, it doesn't seem to be so much the head itself that gets clogged, but the cardridges let in air.
If I have a "real" clog, on or two cleaning cycles fix the problem. If it gets worse with every cleaning run, I loosen all cardridges a bit and plug them back in. Again, after one or two cleaning cycles it works again. My suspicion is that the connection to the printer is not 100% tight. As long wet ink seals the connection, it works. If the ink dries, air gets in.
Maybe that helps the next time. In the meantime I only use my R800 to print invoices and print with my new IPF 5000