Repeated measures ANOVA - Within group

[#1]

I want to do simple 1-Way RM-ANOVA. One group, three timepoints. Is there a difference between the timepoints. Only interested in effect of Time and then pairwise comparisons (Tukey). It's a cross-over design with three different exposures. 

Is it adequate to do this in the Fit Y by X platform? The response variable of interest on Y, and "Time" (session in my case)) on X? I prefer this way making it easy to do post-hoc test directly in the same platform.

Here I can also fit BY group. While there are two groups in the project I primarily want to analyse these separately (one model for one group, one for the other, not interested in the interaction here, while it might be a secondary analysis). 

I.e. 

However, it can also be done in the Fit Model approach. In the MANOVA approach, I would just put the three time points on Y and nothing in the model effect (potentially BY group). This seems to have higher power. Is this adequate? 

In the Fit model univariate approach, I would put the response variable as Y and "Time" aswell as subject[Random effect] in the model effect? This seems seems to have even slighly higher power (smaller P for same data). 

 (And potentially by group)

What's the practical/statistical difference for these approaches? Which is most adequate, for this quite simple design? 

[#2]

Perhaps, In the Fit Y by X it is not treated as a repeated measure but three separate groups. 

[#3]

Or perhaps, this the way to do it, not puting ID as a random factor, and keeping the Least Squares personality?

Which gives the effect tests for Time, and giving the possibility for Tukeys and similar contrasts.

[#4]

I guess this I want to do, as Paris in the video of One factor repeatead measures analysis.