Please consider keeping the deaths separate. When I play co-op PVP and exhaust a hero, I can’t switch over to solo PVP and use that hero there either. They are completely different game modes and should be treated as such. (Much like other PVP events that allow solo and event PVP).
I like this idea. Might I also suggest that for co-op pvp, make it so that everyone is at the same level similar to the draft while everyone get accustomed to the style of play and what not.