I strongly suggest that you take your normalized counts, get the averages of different groups, and compare those ratios to the different designs.
That said, you might not be able to replicate the fold changes from ~ genotype + time well in Excel. What that design does is basically say "Lots of the variance within each genotype/time point is due to the ...
It looks good to me. One think I could suggest is to see the distribution of your data/model (with limma/voom).
After you get the list of your genes with:
top.table <- topTable(fit.eBayes, sort.by = "P", n = Inf)
Maybe you can check your multidimensional scaling (MDS):
plotMDS(your_data, col = as.numeric(group))
Then you can also check with ...