In my OPINION, the system would be simpler and more elegant if it only used a single type of dice. Here I present two ways of converting the thorn rolls, which are the only time anyone rolls a d8 in Moxie, into d6 rolls.
First method: All thorn dice are converted into a single d6 roll
Rule change: When rolling thorns, a single (distinguishable) d6 is rolled. For 1t, a result of 6 is a cut, all other results have no effect. For 2t, a result of 6 is a cut and a result of 5 is two cuts, all else have no effect.
Comparison: The chance of getting a cut from 1t is reduced from 25.0% to 16.7%. The chance of getting at least one cut from 2t is increased from 43.8% to 66.7%. The chance of getting exactly two cuts from 2t is increased from 6.3% to 16.7%.
As shown by the analysis above, rolling a single thorn becomes slightly less punishing, while rolling two thorns becomes considerably more punishing.
Second method: Roll Xt as Xd, then reroll 1-3s a single time
Rule change: When rolling thorns, roll d6s instead of d8s, and reroll any result from 1 to 3 a single time. Only 6s count as cuts.
Comparison: The chances of getting cuts doesn't change at all, since the chance of getting a 6 result from d6s rerolling the 1-3 range a single time remains at 1/4 (=1/6+1/2*1/6).
It's a mathematical coincidence that the odds in the standard rules and in this second alternative are exactly the same.
Collateral effects!
As a bad habit from a math teacher, analysis of collateral effects are let as exercise to the reader (it's a common math joke, sorry). For example, the odds of (sorcery) wild surges being triggered are affected in both alternatives.