Hi eveybody - I fell into the LightCarbon rabbit hole, and am about to order a LCG072-D soon, so I have spent half of my vacation reading a lot here on Chinertown.
A lot, but surely not everything, and so here is my first question:

Can someone tell me what the weight of the down tube storage door is? It looks to be rather weighty since it is aluminum.

I have the latest version of the door and with bottle cage bolts it is 53g.
I just received my frameset 4 days ago.

Just an FYI, I ordered my frameset with custom paint on April 16th and today I received pictures of the painted frameset. So that is 10 weeks and 4 days. Chloe says it will ship tomorrow
frameset size 54 and bars are 400/80.

Currently I have a little over 1000 miles (1600km) and I am very happy with this frameset. Currently the best thing I have bought in this hobby Every time I come to a rough section of road I take it with speed instead of slowing down like I did with my previous frameset. It still amazes me just how much it absorbs. A few weeks ago my cousin and I swapped bikes for a few minutes so I could get some experience with the Di2 shifters that he has. When we swapped back he commented that mine was so smooth it was like riding in a car I have not had any problems with the frame. And you asked if the inserts are stiff laterally, well to me it feels like the power I put out all goes to the wheel. But I am not a pro level cyclist that can put out 1000+ watts. According to the power meter when I was riding my cousins bike, I was averaging 200 to 230 watts with a peak of a little over 500 watts.

Carbon-Speed CS-RB01+RF01 54cm BSA
http://www.xmcarbonspeed.com/Productinfo.asp?f=1391

I ordered this frameset from Peter with a single color paint job. This only took six days to complete. Peter sent pictures just before the order was packed and shipped. One week later it arrived at my door. I was very pleased with every part of the order. Peter was quick with replies and had answers to everything I asked. And the frame and parts were very well packaged.
The frame was made very well. I did not see any flaws on the surface nor inside the head tube. Plus everything I bolted to the frame was perfectly aligned. Well of course not the derailleur hanger, that is normal procedure to have to do the alignment on these.

The internal cable routing was well thought out. It was very easy to fish out the inner cable. Under the bottom bracket is an access panel that you remove. Inside there is a metal plate (on left in photo) that you pull out and this give a large opening for retrieving the cable. Other nice features on the frame include a metal plate to protect the frame in the event something gets jammed between the chainring and frame such as a rock or somehow the chain itself. Also there are bolt holes on the bottom that are in a position that appears to be for a cadence/wheel sensor. Another feature has to do with the cable stops in the frame. They are made to fit closely with the ferrules and angle the cables away from the frame so the cables do not rub through the paint or bare carbon fiber.
Painted 54cm Frame 1039g, fork 384g. Completed bike was 17.5 lbs (7.9kg)  and that is with a heavy saddle (Brooks C17 404g). Front and rear wheelset with tires/tubes/cassette totals 2630g.
I do not have a lot of money to buy the lightest components but that was not the objective of the build. The goal was to make my rides more enjoyable by taking away some of the harshness of the rough roads around here. I now have 200 miles on it and can say on each ride I am still amazed how well this frameset absorbs the rough chipseal roads. Many times I have found myself steering into the rough patches and the dips created by moles tunneling under the roads, just to feel how well the elastomer inserts and frame design work. The sharpness of the sudden jolts are completely removed. More of a bump then a painful impact.
I'm looking forward to many miles on this great bike. My goal this year is to do the circumference of the Moon (6,783.5 miles).