In the last six month my experience was that it plays a role if you make a side for a very popular key or for some "normal" keys. Especially for popular keys the sandbox time has grown extremely. For example some DSL Topics im in the sandbox fpr nearly one year now. For other topics like lokal sport club i ranked after some month.
You are thinking in the right direction but to add to that think about higher quality incoming links for those bigger niches.
I have not seen the keywords playing any part in sand box time. It may just look that way though as I have seen that being sand boxed does not remove your site from results it just penalises it, so for some less targetted words you may still come up even though you are in the sand box.