Note that making your own mailers out of a large piece of cardboard is much easier with a box resizer.

Also, the lady who uploaded that video you linked said she likes to ship any inserts outside of the jacket...but ships the vinyl inside the jacket? oof.

Edit: also, I've had great luck going to record stores, buying an album or two and asking them for a few spare shipping boxes. Never met a shop that wasn't happy to get rid of them. I shipped my (at the time) ~75-record collection cross-country this way, double-boxed inside of generic moving boxes w/packing peanuts.