Lets figure it out then.

If it was your challenge to melt a hole in a sheet of aluminum a mile away over the course of a day. Could you engineer a device (using publicly accessible parts) that could do it?

Here is a consumer built 10kW laser melting stone at 3 or 4 inches away

So what we would need to do is lens this beam in a way that will let us refocus it at the side of the rocket.

Perhaps this is too powerful, we don't need it to cut into the rocket instantly, we only need it to heat up and eventually burn a hole into it. A lower powered beam could be easier to lens safely. A lower powered beam could be smaller and cheaper, maybe we'll build a kit that uses 4 or 10 individual beams converging onto a point at the rocket. This could help with lensing and heat distribution at the device.

We don't need it to instantly reach 660* C at the rocket, only that it eventually heats up the metal to greater than 660* over time. That gives us a lot more room to play with lower outputs and how we lens the beam(s).

I wish I was better at math and I'd try calculating the falloff of the beam over distance to see how strong of a laser we'd need to start with to eventually heat up the aluminum.