We provide details to statistical consultants in two ways.
We have written FAQs that contain a Prism file along with corresponding R and SAS code for one-way repeated measures anova, and for two-way repeated measures ANOVA with repeated measures in both factors.
The fitting of the mixed model is the same whether or not you selected the Geisser-Greenhouse correction. The Geisser-Greenhouse correction only changes the degrees of freedom used when calculating P values from F ratios. So all results except the P value will be the same with and without the correction.