Wow. I've never made it to large hulls before a war is declared. What level are you playing at in those games?
I usually play on Tough or Painful, with gigantic galaxies.
Firstly, this only happened to me in two games I can think of.
Second, I'm not counting my flagship (medium) which I do convert into a warship. Sometimes I can just park my uber flagship around a Spin control center and that's enough to deter my opponents.
Third, I try to avoid all wars, and I also start wars amongst other races so they deplete each others' arsenals. I also brown nose with tributes occasionally, to maintain relations. I will also try to mimic the alignments of my neighbors, so that it's easier to ally with them. I'm kind of a d*ck with allies; I steal all their planets using influence. That's my general strategy for expansion: ally and convert.
You won't typically need soldiering until you've killed the fleets defending the target planets, though.
Fourth, who said anything about taking other planets? If #3 doesn't work, I mutter a few expletives to myself and then start building using whatever hulls I have. Usually my soldiering + high population + my flagship zipping around intercepting transports is enough to muster some defense in time. I play a very risky game, but if I am capable of reaching a certain "critical mass" before the other civs realize I'm a ripe target, I am so far ahead of them that they just can't keep up.
Fifth, a bit of luck I guess (and not the ability).