Your layout looks fine to me.

I don't mind layouts that look more natural and don't have all the houses in a row, in fact, that's what I prefer in my game. In most cases, what makes a difference is just landscaping.
Before you start, it's a good idea to have an idea of how you want to decorate your town. You don't have to have a theme but just deciding on the atmosphere you want (or if you just want to place random stuff you like even if it doesn't all match, whatever is most fun for you) can make a huge difference. If you need ideas on decorating a frog-themed town, let me know, I'd love to help and I have lots of ideas.
Then start by laying down your basic paths. Find a pattern you like and lay down the path between main spots first (houses, Re-Tail, the train station, etc.). After that, you can decide where you want your PWPs and other decorations like flowers to go. Having a path first will make it easier. Even if you're just working on making a natural path, knowing where it's going to be can help you have more structure in your town. You can also sketch or take a picture of your map and then draw the paths on it manually so you can have a plan.
I doubt that you don't have any room for hybrids, unless you just have lots of awkward rocks (and trees but you can remove those and plant sprouts elsewhere). If you really don't, you can just use the beach for that and for storing flowers in general, especially the private beach.
If you really hate an irregular layout no matter how it's landscaped, the only option is starting your town from scratch and plot resetting. You could always try to find someone to hold your villagers for you. It seems like a lot more work, however, and I personally like towns that look more natural.