If I understand this, you'd like a 2-DIN box that plugs into the dash. Except for the plug-in system, that's what I did on my carPC. You'll have to make a couple of additions, and they'd be good on my system, too.
I went through a couple of different system designs before I began work on an open-back, 5-sided box; that starts about post #472 of my worklog (if you're displaying the standard 15 posts per page, that's page 32). The screen mounts on the closed front. You might want to consider enclosing the back, or at least mounting your plug-in device(s) there; you'd have to allow for the intake of cooling air. One option would be to leave it like mine, and plug in your cables before sliding it into the dash. The downside of that, I discovered, is that it takes a lot of dash depth to house the cables, and it takes a bit of magic to get them to curl into place nicely as you slide the PC into its position. A miniaturized, server-style folding cable arm might be very good here. At the least, you'll have to figure out an interface that takes your screen, touch panel, power, sound, and multiple USB plugs into account. I say multiple USB plugs because some USB plugs need to go directly to the mainboard -- wireless, GPS and touchscreen come immediately to mind -- and the rest can work on a hub.
I haven't built the bezel yet, but the plan is to build it so the touchscreen can be removed, a few mounting screws removed, and then the PC slid out, without removing the bezel. The touchscreen is larger in both dimensions than the 2-DIN opening, and the bezel I have in mind will allow that, since I'm leaving the touchscreen in its case.
You'd have to engineer a mounting system that holds the PC in place, rather than screws; a rail system would certainly work. You could also form a cage of simple aluminum angle and mount that in your dash. It could be a track for the PC to slide on. I would think that, if your pull handle was at the bottom of the screen, it could be your locking device; pivoting it somehow would release the PC and monitor, and then it could be the way you get the PC out far enough to unplug everything.
Power is another consideration. I used a panel-mount receptacle on mine. You could do something similar, but I'd recommend using an oddball receptacle that doesn't accept a normal plug. You don't want someone plugging a 12V system into 120V, because that would make terminal smoke come out. Instead, plan to have a small external power supply you can take with you -- a power brick -- so you can plug it in and use the PC. You might even look around for an old power brick that puts out 12V (they're rare) and find a receptacle that takes its plug; use that for your receptacle and use a similar cable to bring in the car power, and you'd be ready to go with no manufacturing issue.
After you've measured the space available in your dash, one good starting point might be to consider a chassis from Blk02si. He has this thread and this thread in the Fabrication area, and a website. He can customize to suit your needs.
If you'd rather build your own chassis, you could produce a design similar to mine using flat aluminum panels and aluminum angle stock. It's a pretty basic design that could be built with minimum tools, and it's certainly strong enough to carry around; mine is overkill -- it would be strong enough with half the fasteners.
Information on tools required is included in my worklog.
I'll watch to see what you come up with. This is a very interesting project you have going, and an approach I might have considered way back in my design phase. I'm more of a manufacturing guy than a programmer, so I'll help you with ideas where I can.