Time offset driver

I’d like to have random animation on an object in XYZ for both position and rotation, and while I could add a noise modifier to all six fields, that feels unnecessarily complex.

What I’d like to do is assign it to x and then use that in all the other directions, but with a timeoffset of maybe 3000 frames or so. That will give the same effect, but with one place to control them, instead of six.

This is super easy to do in nuke. You just type the name of the field plus an offset. So “translate.x+frame+3000”.
I found this thread Driver and time offset which seems to do the same thing, but I can’t get it to work (I’m pretty shit at blender scripting).
Does anyone know of an easy way to do it, or do I first need to learn blenders python api?

This driver setup should work: