First off, I am not really sure that I understand what you are trying to do.
On the point of supporting a cantilevered balcony deck;
We have always gone by the rule of 3X (minimum 2:1). What ever length you intend to cantilever, you extend back in, 2x to 3X that (2:1 - 3:1)...or to the furthest extent as possible.
Link (pages 11-12): http://www.orgsites.com/ct/strober/IRC2003Floor.pdf
b. Ratio of backspan to cantilever span shall be at least 2:1.
c. Connections capable of resisting the indicated uplift force shall be provided at the backspan support.
d. Uplift force is for a backspan to cantilever span ratio of 2:1. Tabulated uplift values are permitted to be reduced by multiplying by a factor equal to2 divided by the actual backspan ratio provided (2/backspan ratio).
e. A full-depth rim joist shall be provided at the cantilevered end of the joists. Solid blocking shall be provided at the
Example: We did a repair on an apt balcony last fall. The deck extended out 6', we carried the joists in 10' and bracketeted to a perpendicular beam. We went in through the floor to do it. We lagged the new PT joists to the interior joists. Installed blocking, sealed exterior penetration points (Brick & mortar with Polyurethane sealant), etc - All inspections passed.
We are planning a large addition this fall, with the same type of arrangement.
As you know - With a permit, you will be required to submit the structural design you are proposing, prior to the permit being issued...So, whatever you are planning on doing, will either be shot down, or, approved, or, may require an engineer's review & stamp.
Again - I am not sure I understand what it is, you are trying to do.