I happen to find myself currently in the position of no longer owning any real estate. I see myself rectifying that down the road, but shooting & guns are such a tremendous part of who I am, that while nothing is certain in this life -- I can say with confidence that the
NEXT time I consider purchasing a home on piece of land, it will be with the intention of shooting on that piece of land. And if that's not possible, I don't see me all to interested in buying it.
To answer your question directly & specifically, I'm not sure if you should feel "guilty" or not, I can absolutely see where you are coming from. If I were you:
No, I would not be visiting 3 miles or 25 miles (or more) to a public range as an alternative. But I can tell you that I absolutely
would be likely to open a conversation with my neighbors, especially the closest of them, and especially if they otherwise seem like decent, reasonable folks.
This is (really) one of my biggest fears of looking for a home to own in the future. I would actually like to do a short interview of the neighbors... to find out ahead of time what I might be up against. I could sit here and puff up my chest and spout about my "RIGHTS", but I'm a good guy. If I could find a place where the shooting (that I will absolutely be doing...) is somewhat less than a complete menace, I'm much more interested in going there.
As a side note, a buddy of mine had a 13-acre place a couple years back before, well, that went away.

We specifically crafted a purpose-built shooting range on it and it was nearly a "dream come true" kind of private range, except for the fact that it was 50 minutes away from me and I didn't own it. The neighbors were
cool with our shooting, but did ask us to suspend the shooting as we approached and were knee-deep in to deer hunting season. Quite simply, nobody liked the idea of spooking all the deer.
Me? I know less than squat about hunting except that I fully support it. Does
massive amounts of recreational shooting through dang near all of the non-frozen months not scare deer away, generally? I have no idea. But when it was time to suspend the shooting at the general request of the neighbors, we were
happy to do that.