I am about to put two new subs (Rythmik F12s) inside a built-in cabinet, and here are the comments that people have generally given me:
1. Most importantly, most people who weighed in think that putting a sub inside another enclosure is an awful idea that will interfere with the sound, create rattling, etc. I am fairly nervous about doing it, but have no choice due to WAF factors. So I would be a little hesitant to voluntarily select in-cabinet installation.
2. With that said, none of the manufacturers I talked to said that it would not work (I spoke to HSU, SVS, eD, and Rythmik). eD had more hesitation than anyone, saying that while it probably would be fine, you wouldn't know how it sounded until you actually got it installed. On the other end of the spectrum, HSU's owner's manual for the ULS-15 actually says that you can place it inside a cabinet.
3. Some people said you have to worry about overheating because of the amps. Neither eD nor Rythmik were particularly concerned about this, though. They said that in the abstract, you might be better off with a fan. But they didn't think it was absolutely necessary. If I'm understanding your cabinet dimensions, that doesn't sound like it will be an issue for you.
4. On a related issue, I was seeing contradictory advice on the size of the enclosure. Some people recommend having an enclosure that is only slightly larger than the sub; this supposedly helps with the sound quality. Other people said I needed several inches of room on each side to reduce the risk of overheating. I don't know what advice is correct.
5. One of the manufacturers said that if you are installing inside a cabinet, you should try to have the sub centered inside the cabinet.
6. I am going with Rythmik F12s. I asked the owner (Brian Ding) yesterday whether I could benefit from using Gramma isolation risers, acoustic dampening materials on the cabinet walls, or something like Rockwool to minimize the acoustic side effects. He didn't think any of those were necessary, FWIW.
7. What type of grill are you going with? I'm probably going with the 3/16 grill from this place:
http://www.reliablehardware.com/customspeakergrill-316diastaggered.aspx
8. People also talked about the stoutness of the cabinet (less stout=more rattling). Some people even said that to minimize vibration one should cut out the bottom of the cabinet and have the subwoofer resting directly on the ground.
As you can tell by my post count, I am somewhat of a newbie, so I don't pretend to have all the answers.