Visualizing signal strength by location

I was able to accomplish what I wanted to do, albeit imperfectly, by just using larger dots in the layer style and rendering with an additive Gaussian blur.

To add that blur, I did the following (QGIS 3.10):

1. Set the symbol size to however large you want the blur footprint to be. (I chose 10mm).
2. Expand the Layer Rendering section.
3. Tick 'draw effects'.
4. Use the star button to the right to open the effects dialog.

5. Add a Blur effect.
6. Set the blur strength to a large proportion of the symbol size. (I went with 7.5mm, 75% of my dot size.) Play with opacity and blend mode until you obtain a visually pleasing result.