I know from experience that a 7 gpm pump will only work on a 20' boom with yellow nozzles or a 13' boom with red nozzles. We have this setup on our Kawasaki Mule. A gas powered pump is the only way to go. But like I said before, look at the output of the nozzles and make sure the pump has more than enough output to handle the amount of fluid that the nozzles are needing.
As for the boomless nozzles, they are great for when there is no wind at all. As soon as there is any wind, your calibration will be way off and you have the chance of drift. Drift is what give us in the industry headaches. We actually use air inducted nozzles to lower the chance of drift on our booms. They make the droplet larger to minimize drift.
If you have any questions, just message. I can find most nozzle charts so you can decide what nozzle would work best for you.
Bob