possible but not as sure fire as peres

MTM, you might want to consider using longer sections to root. Four inches is the bare minimum to prpagate SP, but IME the pups will be much smaller and slower than if you used, say the whole length of your cuttings.

As an example a year and a half ago I got a four foot Ayacucho that I decided to root "loggy style" but it was too long for any container I coud find. I ended up cutting about 6 inches off the base and rooted both pieces separately. The six inch cut has produced a pup that is maybe 8" high and 1.5" dia. The three foot section threw a massive pup that is already over 2.5' tall and nearly as thick (about 4" ) as the cutting.

Just saying that you'll be much further ahead down the road than you would be if you eat most of it now.

So far yeah, just one pup each, but with time, and as they fill the pots with roots they will throw more pups when they are ready. Still a year and a half to a solid column like that from an unrooted cutting is pretty good in my book. It really helps to have vigorous cuttings to begin with and that one was.

Just so you know, my personal record for cactus growth was six feet for a Pedro in one calendar year and four feet for a peruviannus in the same time frame. I had ideal conditions at the time (many years ago now). I just picked up the cactus aspect of the hobby again about three years ago and haven't repeated that success...yet.

And grafting two logs together? Err...ummm...eh, I probably wouldn't do it myself, mostly because it would take time away from the rooting/pupping process, but also because of the difficulty of matching the vascular bundles during the graft. Plus you always run the risk of a graft not taking.