Are the residuals close enough to normality after Box Cox transformation using the MASS package?
max.intercept.BCmodel <- lmer(RTtrans ~ Var1*Var2*Var3 + (1|Participant),data= Data, REML=FALSE)
Skewness and kurtosis seem to be decent
> skewness(residuals(max.intercept.BCmodel))
[1] 0.07592625
> kurtosis(residuals(max.intercept.BCmodel))
[1] 0.863893
I also tested if there was overdispersion which showed underdispersion
> overdisp_fun(m1)
chisq ratio rdf p
1.690057e+00 1.326138e-05 1.274420e+05 1.000000e+00