Thought I'd post an update for those interested.
I believe I've discovered that razing does not necessarily cause all a site's population to flee; sometimes they'll stick around with mostly civilians in a weakened state. This is why I was able to raze Silkendrunken and then squads that were sent simultaneously as part of a different mission to the same site simply came back after doing nothing.
Since then I've been playing with conquest, actually taking over other sites. My dwarves conquered Squaresung, a settlement a short way to the south. I took over Ringcactus, a city of the same size as Silkendrunken (~200) but not surrounded by other elven settlements, which was immediately to the northwest.
Then for even more fun, I decided to take on an elf city about 500 strong. I sent most of my military, about 10 squads' worth at that time, to raze Verseleathered; they brought the population down to about 50, which quickly rebounded to about 75 while all my dwarves were still returning. Once everyone was back, I sent out an additional mission (can't remember if it was pillage or raze) with just one squad. Then, I sent in a squad of mostly losers whose only good fighter was the captain, who I'd called back from a previous conquest. That squad took over, and the captain now was the new administrator so I couldn't reuse him anymore.
Winter passed. Spring arrived and another annual elf siege showed up to get slaughtered on my western border. I've taken to saving most of their clothing, even the wooden shoes, because dwarves can apparently make do with elf or goblin clothing in a pinch. I save their crap weapons for traps, and discard the rest of the wooden shields and armor.
Finally I set my sights on Silkendrunken. With the siege cleaned up with a lot of help from DFHack, because I'm lazy and don't want dwarves traipsing all over the map for this junk for the next two years, I sent a raze mission of three seasoned squads to Silkendrunken. The population of about 200 didn't budge, but the raiders were successful in killing about 30 elves. Leaning on my theory that Silkendrunken was now ripe for the taking, I sent in another squad of nobodies. (Some of them were legendary observers, but had no serious fighting skills yet.) To my surprise and delight, Silkendrunken fell to the invading forces of the Faithful Chamber.
So this seems to be the solution: If raze doesn't cause the site's government to flee, it may still have done the job of destroying most of that site's army. Following up right away with a conquest mission is likely to succeed in this case.