Ring height with Tenebraex cover

[Str8shuutr45]

I am posting because I can't find any concise information on the interweb. I have a Leupold Mark 5 HD with 56MM objective lenses. I just ordered Tenebraex covers for it and think that the current rings are a tad too low. The rifle is a Sig Cross PRS with 20 MOA rail, the rings are Leupold ultra-high rings. The Leupold supplied covers scrap across my handguard when opening or closing. I am sure the Tenebraex covers won't fit.
Will I have to use an integrated mount/ring combo like LaRue or Badger to get the scope high enough? I ordered the covers at Armament.com. They told me the OD of the objective covers is 2.78".
Thanks in advance.

 

[pineoak]

The "super" highs are 1", do you have a specification for those rings?

 

[Str8shuutr45]

This is what I know...the mid-point from the top of the hand guard to the middle of the objective is 1.425"
The OD of the scope is 2.545".
Would I be okay if I went with a ring height that is >1.4" from handguard to middle of the objective? If that's the case, what are my options for a good ring or mount combo?
Thanks again for your help.