Small backyard pond overflowed after heavy rain—how can I redirect the water without digging?

I built a small backyard pond last summer using a preformed liner and some aquatic plants. It’s about 4 feet across and maybe 18 inches deep. It’s been great for attracting birds and frogs, but after the past couple of heavy rainstorms, the pond overflowed and flooded part of my garden bed next to it. I don’t want to dig up the whole area to install a drainage pipe or a big trench, since the garden bed is full of perennials I’ve been nurturing for years. I tried placing some rocks around the edge to slow the overflow, but the water just pools and eventually spills over anyway. Ideally, I want to redirect the excess water somewhere safe without disturbing my plants or doing major landscaping work. Has anyone dealt with this kind of problem before? What simple options might I have for managing overflow from a small pond without heavy digging? Would a rain barrel or a French drain alternative work here?