Overlapping text has been a problem for years, you realign them then they overlap another text that you have Un-overlapped.
Any way if you take the text and say make into Mtext with color then it will be stacked automatically, this would be easiest. So confirm that is Ok.
Other version would be just to stack the text based on the text height. The only problem is if the text is annotative then it may move depending on Anno scale.
So choice is yours but need a sample dwg, looks like the text is in different layers so need that result order, a before and after sample.