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It "might" fit in the doors but should you is another question. From the specs I read, it needs to be in a small sealed enclosure which you probably won't get out of the doors. It may sound OK being "free air" but normally subs not designed to be free air sound like crap when not in a sealed box and/or could cause damage to the voice coils.
Depth is OK, 9 3/8" cutout will require door to be trimmed but should fit, but the top is where you may have an issue. The door skin doesn't have much room around the front where the sub would be, I'd bet against it fitting.
Also, as mentioned, wouldn't work too well in the door. it would essentially be treating your door as the box, which is way too big.