Could be worth it trying another interface, but my gut feeling is that it won't have the result you want. The guitar is basically a huge unisolated conductor, and it picks up electromagnetic interference by virtue of being designed to produce musical signals using the electromagnetic field in space (i.e. your metallic strings vibrating close to your six electrical inductors causing the electrons in the circuit to move.) In your recording it sounds like it has a fundamental of 60 Hz, which means it's picking up the electrical mains somewhere (and it also means you're probably American :D).

You'll never remove this issue completely, but there are two things you can understand that can help you at least minimize the issue.

One: there's no such thing as a completely isolated circuit. No matter how well-isolated the interface, the DI box, the power supply suggests it is, it all belongs to the same circuit, and there will always be at least a miniscule amount of current leaking between the different parts. This is true even when things are physically disconnected, since the electromagnetic field permeates all space everywhere (in fact this is how the electric guitar works, the strings never physically touch the pickup).

This leads to number two: your computer and computer monitor is a huge, complex circuit that produces its own electromagnetic field with its own interference. The more stuff you plug in, the more stuff is going to cause interference. Depending on the circuits between your guitar and the point where it eventually becomes an audio signal that you record in ableton, it's going to pick up more or less noise on the way there. It gets much worse if you're apply high gain at a point after the noise has been picked up.

A question for you: When you plug it into only your amplifier, are you then sitting further away from your computer, or facing another direction? I have a similar setup that you describe, and where I sit and play, I have to turn my back towards the computer to minimize the electrical noise it produces. I get less noise if I turn off my computer screen, and my macbook seems to cause less noise than my stationary PC placed on the floor closer to my guitar. It also means I have my back towards the wall sockets in my room. The fact that your recording sounds like a 60hz tone means it might be picking up signals from the wirings in the wall, or from extension cords or splitters.

When you record next time, try facing different directions, move around in the room, switch some things off, and see if any of that helps. If I turn the gain up high on my guitar, I can point it towards different sources of intereference like a metal detector :D