The attic is about 1700 SF. I have no idea what the RPM/CFM exhaust of the
attic roof fan is, and there is no legible mfr ID on the fan.

The attic insulation seems to be the cellulose type stuff at a depth of about
2".

My question is, what do I do to cool us further? Would adding some sidewall
vents farther away from the fan help the airflow? Small vents, like the 6x8
panels at Lowe's/HD? Or is a very large additonal exhaust fan in order?
Should I add more insulation? I'm really just stabbing in the dark here...

If the attic is 1700 sf, then you need a minimum ventilation area
of around 6 square feet of ventilation area, evenly split between
intake air and exhaust air for passive venting but I don't know how
that changes for powered vents. In any case, if you only have
the exhaust port, and no intake vents, then the attic is probably
sucking cooled air out of your living spaces to replace that blasted
out the power-vent. So yes, you need sidewall vents, or soffit vents,
or something. The other thing you need is about 10 more inches
of insulation on top of the existing 2" cellulose.