I would be tempted to just use construction foam for a lot of this build. Its not all that expensive and its rather easy to work with. A dremel will carve out areas quickly with a cutting attachment and a plane sander would work good also. A couple coats of clear enamel before you try to add any Bondo or fiber glassing would be a good idea also.
For maximum strength on the wing supports, I would suggest using a solid wood frame like 2 x 10 for the actual wings and internally attach them together to give the whole thing support. I would build the wings 1st and attach them to the biggest baddest piece of PVC you can find for the tips.
Once you get the skeleton frame up for the wings, then you could start looking at shaping them more properly. Some might say you should shape them before you assemble them... but seriously you would have to constantly hold them up to see how good they look anyhow. Get them to a close approximation I could see that after that an electric plane sander would shape them fairly easy if you use a very gritty sandpaper.
The wings are going to hold the bulk of this things weight, even if you manage to find a way to suspend it in the air, eventually you will need to transport it and having the most solid wings you can engineer wouldn't be a bad idea. I could see it now, you get it all built and have to transport it on a flatbed car trailer... you decide not to use a tarp to cover it and cause like 100 accidents from the stares...
You may want to fabricate some attachment points on it for things like aerial suspension or for mounting removable wheels under it.
For the canopy, you might look at using those dome skylight window covers you can buy at many hardware stores. It might be a little more expensive to go that way but if you attach 2 of them together they should be approximately the right size already.
Using cardstock for a much smaller scale model would be the only way I would go about using cardstock. You would have an unimaginable amount of warp-age if you build the large pieces out of cardstock. The wings for instance... they would bow down something fierce. You would almost have to build them 1st then attach them to have a chance of not warping them. You would go through like 1000 pages of simple reinforcements to reinforce this beast.
Al alternative method to using wood would be to use heavy duty PVC. A little work and you could get a full sized skeleton up.