As with Rightycomplex, I don't think you'll need one of the really big oilers to do the job on heavier lanes. The speed and rev rate can allow you to get through with one of the medium-heavy balls just fine.
For your heavier conditions, you may want to look at something such as a Storm Marvel, Roto Grip Outlaw (recently discontinued but still available). All of those can cut through some heavier conditions and should still make the turn downlane. Also, these are all symmetrical cores, which can potentially fit you well. If you go asymmetrical, something like the 716T from Track, 900 Global's The Look can fit the bill, or the DV8 Hell Raiser hybrid. That may be as strong as you would ever need.
On the mediums, potential options include the Roto Grip Bandit, Storm Victory Road or Tropical Heat (hybrid), 900 Global's Sure Thing, anything in the Track 503/508 lines, or the DV8 Reckless or Marauder. All of these offer symmetrical cores and have a wide range of options from angular to traction motions. It will depend on the motion you are looking for in all honesty.
On the lighter conditions, you could take a look at the Storm Tropical Heat (except hybrid), Roto Grip Shatter, Track 300A or 300C, 900 Global Hook, or the DV8 Misfit. Key is to have something that will be clean up front and still give you a predictable move on the back.
As always, the best thing to do is work with your driller to fine tune the options. But, at least this will give you a starting point on what may potentially work out.