Having GV as part of your main gmail account has advantages of already being signed in to voice, etc. Not insurmountable, but certainly seems annoying to have to make a separate GV account.
Not a solution, but perhaps at least to help from missing chats that you received when you weren't really online, I built a bit upon tylercal's idea:
1. I created a label called "orphanChat"
2. I used gmail's multiple inbox feature to show me the results of this search right below my inbox:
in:chats -me -in:orphanChat. This shows all new chats which I never responded to.
3. In order to remove chats from showing there, I either need to reply to them, or label them as "orphanChat". If I do that consistently, then that mailbox will always be empty except when I really have a missed chat.