Some event specific ideas:
NA v EU show match: Bid war to decide server location (which side has a ping advantage)
Depends on your format, if you are just playing one map it would be less viable (but still possible, would have to start the bid war before hand). Anyway, ping is always an issue for these, and typically they are played over three maps alternating between and EU or an NA server. If you are using the same format (and have access to both an EU and an NA server) then creating bid wars to choose which server is used (make it into an NA v EU for the viewers as well). Could do this for all maps, or just for the decider.
Jump/Surf: Bonus runs, record attempts, etc...
Would have to leave these up to the players taking part, they would need to be comfortable with the potential bonus runs. But bid wars to determine from a list of options, for this extra content. Or, make it a series of goals. Each subsequent goal unlocks an additional bonus run.
1v1 MGE: Select location, either for all matches, or for brackets/individual matches
Depends a bit on the format you are planning on using, and depending on classes being played the options would have to be selected carefully. Alternatively, could allow viewers to vote for classes/weapons to be used, but that has the potential to get clowny (which might not be a bad thing)
Pubs are fairly straightforward. Selecting modes, maps, custom content, can also allow players to bid for early access prior to events that will appear on stream. Or, if you have several pub servers live you could allow viewers to vote for which server appears on stream for a set period of time
Uncrating, maybe selecting the series that is uncrated. If you are doing all at once this probably doesn't work. But if you aren't uncrating everything it is viable, or if you are uncrating at various times it can also work.
Ultiduo/BBall: First thought was map, but there isn't a huge difference between maps for either mode. Might be interesting to vote on teams comprised of the various 'stream personalities' present to be played after the main event. Sort of a more clowny show match involving the various twitch and youtube personalities that are present for the event.