I cannot help you out with the question on the casting style, but, as soft as regular round lead wire is, I would think you could cut off a piece the length you need and just flatten it.
As an experiment, I just now took a piece of round lead wire and adjusted my vise jaws and flattened the wire by inserting it in the jaws and closing them. Did not take long at all and flattened it nicely. Just something for you to try if you already have round lead wire.
It is a singlehand spey cast modified a bit… He also is doing a bit of just quick normal casting but with enough wind from the side to keep the tailing loops from connecting with the fly line. Note the line is going behind him when he casts in the semi-normal fashion, but not when singlehand spey casting.
The Belgian cast when viewed from above is an open “C” on the downwind side. Just get the line moving and swing it around you. A snake roll is a set-up to a spey cast. I did not watch the whole video but did not see a snake roll. On snake rolls and Belgian casts there are no false casts behind the caster. The Belgian cast does start behind, but the snake roll stays in front of the caster the whole time.
As suggested above I just roll my lead wire flat with the SHHAN bottle usually, It only takes a quick roll or three to make nice workable “tape” that is hard enough to stay put.