What reason does your handyman give for needing a second fan in your attic? What's going to be different for your house? I'm assuming your attic is a typical uninsulated attic in the US. I live in Texas, and as far as the eye can see there are houses with uninsulated, passively-ventilated attics. Almost no one has powered attic ventilation. I have a thick layer of blown-in insulation up there, and with the volume of air your handyman wants to move, I'd be concerned the insulation would move with it.
In an ideal world, all our attics would be inside the insulated envelope of our homes, but our building standards are not there. So where you can affect energy efficiency is in improving the impermeability of your insulation as it currently exists. If you're going for energy efficiency, slightly lowering the ambient temperature of your attic in the summer heat is just not an effective solution. Spend that money instead on fully sealing all the holes around joints and fixtures that are currently leaking air between your living space ceiling and your attic, and improving the R value of your attic insulation.
I don't know if what I'm talking about applies to your house, but if so, check out this Matt Risinger video for a lot more detail.
The reason the handyman gave for installing two fans was basic, to improve the dispersal of hot air. My partner and I concluded that removing heat would be the most effective first step to decreasing the temperature of the house, but we can be talked into considering insulation first. We'll look into leak patching and into insulation.
Do you happen to know if during the winter months, if insulation would significantly block the house from being heated by the sun? We are looking to get a heat pump in the long run and originally planned to have the insulation done at the same time, but in the meantime, winters can get cold here and any heat we get goes a long way.
Improving the insulation barrier between your ceiling and attic will only serve to increase your home's heat retention in the winter. When it's cold outside, the sun heating your attic is not going to increase the heat in your home more than the cold ambient temperature in your attic is going to decrease it. Before you pay to have this work done I'd genuinely consider whether there are other projects that would be much more impactful you could do instead. Definitely get other opinions from contractors first (never just get one quote for any project, prices and recommendations can vary widely) and see if you can get a certified home performance contractor to take a look at your goals