I would like to suggest a mixture between OHBs and major battles:
1 day announcement only revealing the used format
1 day submit phase when the whole bitpack with samples/restrictions/themes is revealed and entries can be submitted
1 day of voting

This battle type could also be used to promote rare or new formats since all interested BotBrs have one day to prepare.

Another advantage is that everyone who wants to take part in this should be able to because s/he has not to be online at a specific time to even know that there's a interesting battle.

Practical, given that not all BotBrs live in the States (like me D:).

How about calling it "All-Day Rumble" (ADR)? Not quite a catchy acronym, I suppose, but anyways.

Not the first time this idea has come up, if I am not mistaken! I still like it and would be down for it.

Well, my researches only found a thread wishing for variable OHB lengths... :-)

Say, an OHB in 145 minutes? Sounds kinda out of context.

Yes, these are things previously discussed. While it wouldn't be too hard to modify the OHB engine to do different length battles or to set it one up days in advance, I haven't because, as brightentayle stated, it's "kinda out of context." The only code I'm willing to do on the current incarnation of BotB is bug fixes and security. I am working on a new version of BotB with an optimized code base that I will soon be sharing with certain BotBrs for hopefully increased production and development. ;)

So, would that mean (slightly) easier implementation of the new formats and compo types?

Entry formats are already pretty easy to create and edit.

The idea is that instead of there being a separate system for each battle type, there should be one very flexible and extensible engine.