Rods Puzzle

Hello everybody!

This is my first Puzzle design in fusion360 and I really need some help!
The design itself is exactly how I would want it to be but there is one problem... it is impossible to print without supports, and even if you print with supports it is impossible to get them out...

The purpose of the puzzle is this:

There are four rods, one on every side.
The bottom part can turn and move up and down.
You can't open the box completely until every rod is removed.

Like I said there are some problems in the design and I would really love some help and/or suggestions:

Many many maaany overhangs.
Puzzle part will be visible when opening.
Rods will be fragile because of their size and scaling will be nearly impossible because he box itself will grow enormous.
The InnerBody and Body will have to be combined before even try to print.(Dual extruder and solvable filament for example)

I am new to 3d modeling and if anyone dares to take a look at my design.. I attached the f360 file in the downloads.

Thanks in advance!