I'm just starting an install on my 2001 civic as well. I found that the 2005 Civic Special Edition dash bezel has a double DIN sized radio opening that fits the Lilliput fairly well if you take the plastic housing off. I haven't checked it myself yet, but the 2005 is supposed to fit the 2001 dash perfectly. I've eyeballed it and I agree. Plus it recesses the screen about an inch back into the dash which should help with glare. Here's a link to a pic. The only difference I can see is the SE has silver-faced "control bars" on the fronts of the vents...my 2001 does not. But, it looks like you can unscrew the vents from the back side of the bezel and swap them out.
What I'm planning to do is just install the touchscreen and circuit board without the housing. Fill in the gaps with Duramix and be done with it. Should make for a much easier dash fabrication compared to hacking up the 2001 bezel.
Good luck with your install...I'll be following your progress!!