I would use a mixed grip when grip is the limiting factor. Mixed grip will still work your grip.
Also, I notice you are concerned about strength loss. At the strength level you are at and the bodyfat you are at (>12%) there should be minimal strength loss while loosing fat. With the right program and diet there is no reason why you can't gain strength in this stage.. Especially in the deadlift which is a lift not very influenced by loss of weight (unlike the bench press). I would take a good look into your programming first, then make sure your deficit on your diet is not to high.
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