[3.19] HH + Omni: Phys or Ele?

I got lucky and found a Headhunter, and would like to try a Deadeye build with HH and Omniscience. I've never played a bow build so I don't really know what I'm doing, but I'm stuck because everything I've been reading suggests HH benefits most from Physical builds because the stolen mods add extra ele dmg scaled off of physical, but I can't find a single physical Tornado Shot guide - they're all ele.

Should I just go with ele, and the headhunter buffs will still be good enough, or try to improvise a physical build on my own (probably won't be great)? My goal of the build is fast mapping / farming.

My budget for now is around 20 divs for everything other than the belt and amulet, if that affects the recommendation. I could also farm a bit longer on my main for a bigger budget if needed, but was hoping to re-roll sooner rather than later.

Thanks!

good ele bows --> cheaper
good phys bows --> more dps

ele bow + hh is more than enough if budget is a concern