How to put LEGO together upside down
I attempt to create a searchable index of SNOT techniques, as this is called. Of those, the strongest 180 degree stud reversal are probably one of these:





If you want to connect the two curves together bottom to bottom, you should be able to do it with an axle, sort of like these two techniques:





If that doesn't work I once had luck playing around with a lever and a rubber band. It was tricky, but it did work: