Paul,
First off, Charles River R/C has some more details:
http://www.charlesriverrc.org/articles/apogeehlg/markdrela_apogeehlg.htm
The information is dated, but useful. When it comes to making that fuselage, you just start cutting wood to about the right size and cut and sand until it's right. I didn't do the tapering in width that Drela did. The fuselage sides are 1/8", and the core is 4 layers of 1/8". I hollowed out bits of the 1/8" sides to clear the servo arms. Basically you cut out your fuselage sizes, having laid out your electronics together to ensure everything will fit, extending the nose as necessary, and then build up the core on one of the sides. The boom gets installed when you have two layers of 1/8" core material in place, then you build up the rest on top of that and glue on the other side. The wing leading edge pin is supported by some plywood (I just used 1/32").
I can't compare a pure Apogee to the bug other than to say it's probably better, but you have to update it to a cruciform tail unless you're purely doing slope soaring. If you're only going to slope soar with it, go all the way and make a balsa Apogee 36 wing with ailerons, as it's a cleaner setup. Otherwise build a built-up wing, as it'll give you the lower sink rate. Regardless, I do know that the Bug likes really low wingloadings. My Apogee fuselage came out about 10 g lighter than the stock one, mainly because of lighter tail surfaces and a lighter boom. It's not all aerodynamics, but the model does launch higher, which is a function of aerodynamics, so the Apogee fuselage is definitely better (and stronger). Basically you want to use the lightest balsa you can find for the tail surfaces, and the boom needs to be made from the good stuff if possible. Thin wall 3/16" CF tube minimum. Don't use smaller diameters--they will explode spectacularly after a few hard throws, and in the process the wing gets ripped from its mounts from the side loading and lots of pieces go flying about.
If you're not happy with the LightninBug, it's time to consider a different airplane. Go on RCgroups and look up the Mimi. It is in all honesty a much better airplane anyway, but there is a little more effort required. You'll have to email the designer to get the plans, as he for whatever reason doesn't like to have them out there for download (they are free at least). Anyway, it's not any harder to build than a Bug (probably easier, actually), just takes more sanding and more wood. I don't know the details, but some well known competitor used one to beat a bunch of Elf's a while back, which is a major achievement and speaks to the capabilities of the design. A number of folks have built them with ailerons too, so it pays to spend the time to go through then voluminous Mimi thread on RCgroups--you'll get to see a huge number of mods made to the design. Most folks are building them to 180 g or so, and it's a capable flier out to 230+. If you've got good wood and some fiberglass to secure the high stress areas, it can be built down to 120 or so, at which point it's basically an Elf without the nasty effects of excessive wing taper or the gaping hole left in your wallet.