As of this patch, while Rejuvenating Aurora is activated you can melee during Singularity
Point Blank and Pristine Emblem are added to increase melee damage (as 50% of your bullet damage transfers to total melee damage)
Make sure to use Rejuvenating Aurora before you dash jump or else Arcane Surge won't proc on Singularity
With only Duration Extender, you can get 3 melee hits while in your ultimate; which can be increased to 4 with Arcane Surge and Superior Duration
This will 100% be patched out within the next few days so try it out while you still can
g59.vision on Discord if you have any questions or tips for the build.