Have I cooked my caps?
Those caps with the rounded tops are bad.  They may act fine and appear to be within spec for now, but they are already damaged.  There is no telling what they might do when.  You should replace them now.

However, replacing them only solves half the problem.  You also need to find out how this happened and then what to do about it.  250 degC is only 482 degF, which should be within the soldering profile of these caps.  Keep in mind that temperature is only one component of the soldering profile with time also being very important.  250 degC or more for a few seconds is probably fine and expected.  250 degC for 30 minutes is way beyond the spec.  If the datasheet does not specify a soldering profile, then talk to the manufacturer or use different caps that are properly specified.

A few other points

Are you sure these caps are genuine?  Yes, counterfit caps do exist, especially in the far east.  You may think of this as a gentleman's game, but there are many many dirtbags in far corners of the world that see it as a quick opportunity and are quite happy to perpetrate deliberate fraud.  To them it's just business.  Make sure you know exactly who you are buying these caps from, and who they buy them from.  You can trust major distributors like Mouser, Digikey, Newark/Farnell, Avnet, etc.  However, unless you have a personal relationship and have spent significant time there personally, you can't trust Wong's House of Discount Parts, probably called something very different when doing business in North America.

Are you sure the temperature really was what you think it was?  Check the oven with independent measurements.

Are you sure the damage was thermal?  Overvoltage or reverse voltage can also cause this symptom.  Note that reverse voltage could be from backwards installation.  Are you really sure the silkscreen is correct?  Are the caps actually installed according to the polarity on shown on the silkscreen or the drawing?