Shorting the output ports which have nominal bandgap voltages of 1.24V
I don't think this is a good idea.  I agree with Russell in that I don't see this causing any damage or running the chip out of spec, so you can always try it.  The reason I don't like this is because the output current is set in part from the current out the IREF pin.  Each chip will have its own voltage source it tries to drive that with.  The ones that happen to have a little higher internal source could drive a disproportionate share of the current out their IREF pins when you really want each IREF pin to be sourcing the same current.  The chip does seem to have some impedance in series with the voltage source which will mitigate this effect.  But, I just don't see the upside.

Your cure is worse than the problem.  Giving each chip a separate resistor is the easy way.  Resistors are cheap and small, and the traces stay local to the chip.  With one global resistor you have a bigger routing problem that may end up using more board space than the local resistors.

The only way that this makes any sense is if this is a very high volume product.  In that case, each resistor costs under $.01, so the savings will still be minimal.  In a lower volume product it's not worth trying to play these games.  You've already wasted more design time on trying to get away with this than you'll ever get back unless you're going to sell many many of these units.