What is the easiest way to increase the Voltage output of this power supply?
The 60 % seems an unnecessarily severe requirement, given that mains voltage has a tolerance of only 10 %.

You can place the secondary windings in series instead of parallel, but the power supply will become very inefficient: 12.6 V AC rectified gives maximum 17.6 V DC, then the efficiency of a linear regulator is 3.3 V/ 17.6 V = 19 %. At 100 mA load the NCP1117 will dissipate 1.5 W.

If you do want to have 3.3 V in a relatively efficient way at a wide input voltage range you can use a switching power supply like this one by Recom. Input voltage range is 90 V to 277 V.  This is for 1W or 2 W, but other modules with higher power outputs are available .