A little bit of piping gel painted onto the cardboard would work as well.
Gumpaste Glue = Tylose + Water. It's also known as edible glue. It is very thin and watery, so I would be very careful putting that on cardboard (paper) because it could compromise the structure if it is too wet. I would stick with the icing or piping gel options.
I used jumbo size ice cream cones for my Tangled tower a few days ago (someone else's idea on this site) and it worked out very well. Added 4 dowels inside the bottom cone...no worries about collapsing. The only way I know to glue stuff together is with melted sugar (that's what I've used on gingerbread houses) so I that's how I got the dowels to stay in place...forever. I also glued the cones together the same way.
Since this was my 1st buttercream/fondant cake, I also didn't know how to get the fondant to stay in place. I left it extra long in both ends and then wrapped the ends inside the ice cream cones (since the cones were glued together back to back, it left the ends open). No problems, but now I know that I could have/should have used some buttercream for it.
WalMart, Smith's (Kroger)...I see them everywhere in my state. WalMart had them in the beginning of the bread isle, by peanut butter etc. I used Joy brand...just make sure it's the "jumbo cups" or "cake cups (even larger)" for your tower. I used regular Keebler sugar cones for the trees...those are usually at the end of the ice cream isle. Good luck 
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