I’m trying to do sheet mulch for the first time this year and so far it is working out well. I’m doing it in my Haskap bed and my Gooseberry bed. We will see how long they are able to suppress the weeds this year. my only concern are invasive grasses creeping over the edge, but a string trimmer should keep that at bay. my haskap bed is a foundation planting and one thing I noticed before planting is the cardboard also acts like a wick, pulling water that lands further away from the foundation closer towards the wall where it would otherwise remain dry under the eaves.
I think that corrugated should work beautifully for the job, although if you have the time and resources, collecting free cardboard should work just as well too. I would go with one layer of A flute, but that’s just me. newspaper in 5 sheet thickness or a single layer of 60# Kraft paper should work as well, although I expect corrugated cardboard to be much stronger at repelling weeds and the airspace may help retain moisture underneath (just an educated guess).
good luck and keep us posted on your test. would love to see some pictures!