“A bird in the hand is worth two in the bush.” I think you have already determined the odds on drilling being able to get more water. It is a crapshoot. You might spend 3K on the well and get better water, or not. It could possibly even make your well worse. Your well already makes 2 GPM, which is 2880 gallons per day, and is the same as the overflow from the neighbors well. It seems you would be better off to store your own 2 GPM, than 2 GPM from the neighbor’s property. I would also leave the well set up as a backup for the booster system. If the booster system fails, you could open a valve and have water, although somewhat limited, directly from the well.
I would avoid having to get water from a neighbor’s property if at all possible. I would also avoid possibly messing up a perfectly good existing 2 GPM well. I know storing water is a pain, but it is better than not having any. You would be surprised at what you can do with 2 GPM.
I have a well that only makes 3 GPM. I only store 250 gallons for a booster pump to help with peak demands. I run two houses, a heat pump, do quite a bit of irrigation, and still feed a stock/fish pond. I just have to start early and stay late to get the irrigation done. And you would be surprised how far 2 GPM will go with a drip irrigation system.