Importing and rendering Esri dot-density data in QGIS

I’m not a professional digital cartographer. I’m a graphic designer who has had to familiarize myself with some processes to fill a real estate broker’s needs. I only offer that as an apology for any ignorance you may read in my post. I’m fairly ignorant!

That being said… I’m having some issues rendering population in the form of dot-density in QGIS 3.12.

• My process begins with generating the population data in ArcGIS Business Analyst Online. (The client relies on ArcGIS for the
  entirety of their demographic and mapping data.)
• I share the data out to ArcGIS Online, where I render it as a
  shapefile for download.
• After download and extraction, I drag the shapefile into my QGIS
  project, where it successfully appears in the layers palette.

From here, I’m encountering some issues. I’ve researched online, and there only appear to be a couple of tutorials for processing the dot-density map that aren’t ancient.

• I select the appropriate layer (pop_density_greater_houston_2010)
  and, under the “Vector/Research tools” menu, select “Random points
  within polygons”.
• Select the appropriate input layer
• Points strategy = point count

• However, the tool does not give me the option of selecting from which
  field to pull it’s data.
• I’ve tried changing symbology to “Categorized” and “Graduated”, then
  classifying based on the density field before running the “Random
  points…” tool.

Results I’ve encountered:

• “Invalid geometry” error messages
• Endless processing (based on the processing animation at the bottom
  of the window)
• single points within each census tract

I cannot seem to accomplish a true dot-density.