How would one conduct a post-hoc test after a significant interaction to determine whether the differences in cell means for one level of an independent level are equal to the differences in cell means in the other levels of an independent variable?
A simple thing you can do is slap some confidence intervals on point estimates in your figure. Keep in mind when you do pairwise comparisons, many people will correct their level of significance to address risks of false discovery during this process. These action will impact your precision estimates on the point estimates and may show interaction effects tending towards 'significance', but no longer below original alpha cutoff. This is an impact of traditional null hypothesis testing.
There was an error in my question and that's why I attempted to delete it as it was misleading. I figured out that you can do this type of analysis using the mcp2a function in the WRS2 package. However, you have to set the trimming to zero. Here's a sample output.