Did everyone declare war on you or is that only when you approach ascension victory? I don't think the game tells you when you're approaching ascension victory. All I know is that my diplomacy cratered at some point so I ended up in a galactic war.
Did you clear out your starting sector and snowball from there or did you maintain relations with some neighboring major races?
My game was pretty war-happy. Everyone seemed to be at war with everyone else. Originally the Altarians were leading in Prestige points, followed by the Manti. They held it for a long time, then they lost it to the Torians, and I took it from the Torians and won. Amongst the above races, I do not think that being on the Prestige track really caused any wars since everyone was fighting everyone anyway. My galaxy really was full of a bunch of belligerent jerks the whole game..
I actually did not snowball after taking my sector. The dynamics in the neighboring sector were better and I was actually fighting a war there before attacking my Alterian neighbors in my own sector and fighting a war on two fronts (first Terrans + Iridia + Alterians, then just Iridia and Alterians). Cleaning up the Onyx in my sector after the Alterians folded still took some time (although they didn't have a chance), the Xeloxi (also in my sector) were always at war with someone else, so I cleaned them up last. By the time I took my sector I'd already snowballed anyway - having the place to myself was more convenience than necessity.
Hope this helps..