I'm sure you get some other replys from some of our expert build community, in the mean time here's my advice.
Take a look here http://www.hexcel.com/resources/technology-manuals
, specifically the sandwich design and fabrication ones.
By just bonding a block of h/c (honeycomb) in an open bay you get no structural benefit. Look at your example chassis above and one of square bays. If you put a load on your chassis that bay would try to "longinize" or deform from a square into something else (parallelogram, diamond, etc.). If you riveted a skin (aluminum, composite, etc.) all the way around the periphery of one side of the bay, assuming you sized the skin thickness and fasteners correctly, you get some structural benefit. Now when you apply a little more load to your bay the square is going to longinize, and the skin will buckle. Add another skin to the opposite side and you get more structural benefit, but the skins are still going to buckle. Now imagine you had something inbetween those two skins that was fastened (bonded) to both skin faces that would keep the skins from buckling.............welcome to the world of h/c sandwich panels.
Now the part were an engineer earns their money. Size the tubing, skins, honeycomb, fasteners, adhesive, surface prep, etc. to optimize weight vs. strength.........and also don't make it cost a fortune.
Don't let me or anyone elese deter you from this construction method. I'd love to someone get this work for our chassis, without costing a fortune. For me, I think a sub 100lb chassis is what you have to shoot for........since most people can build 125-150lb steel tube chassis all day long.