that is slow for peyote in cultivation. i think the reason why most people say it is that slow is because they don't have very good light/environment for them, usually because they are (unfortunately) forced to grow indoors. but 2 cm is doable in a year in better conditions...to a point.
if you want them faster, cut the tap root, this will force more little roots t grow, which allows them to take in more water. i have not had great luck with commercial fertilizers but the last year have been trying commercial bird poo (supposedly for cacti...?) and they are growing like stink!!!
i use a finish sand base mixed with some grit. perhaps the size that will go through an 1/8" screen but not a fine mesh, if that makes sense.
for grafting, if your plant is already planted and settled in than grafting is pretty easy. go buy a grafting stock (the bottom part). look for an actively growing columnar cacti, i like Myrtillocactus geometrizans personally, and it is very common/cheap! many other types are usable as well, people here will probably recommend san pedro as well. with a 3" scion (top of the graft...your peyote) you will want a good sized root stock (bottom). try and find a stock that is around 12"+ tall and 2" ish thick, if you can. you can tell they are growing because the top (new growth) will have a different colour than the older growth at the bottom (usually more silvery/bright).
You will need a thin sharp knife, tissue paper, 70%+ alcohol (iso/ethanol are ok, get it at a drug store or something), electrical tape.
make sure everything is clean. take some tissue and put some alcohol in it and wipe down your table and knife. alcohol is nicer than fire sterilization cause it evaporates fast and leaves no residue. fire is hot and you need to wait for the blade to cool.....then bad things can land on it and its dirty by the time its cool. my opinion....
but let the alcohol evaporate (5 seconds?) before cutting, it will harm your cactus as well....
start by cutting your grafting stock at a wide place in the NEW growth. make the cut level/flat. then bevel the ribs. meaning on an angle from where the skin starts cut down the ribs 2" or so. so it appears pointed a little bit but flat of top. on the top cut another little sliver, a few mm thick, and leave that on top. this way your cut underneath will not dry out when you are screwing around with the peyote. drying out is not the best thing.
snow cut your peyote above the ground leaving a few areols on the roots so it can pup again. make sure you cut it flat.
you will notice on your cacti there is a ring of small dots. these carry the water/nutrients to the plant. all plants have these and cacti are easy to see and generally in a circle. take off that sliver on the root stock and place your freshly cut peyote top onto the root stock. line up these rings on the 2 cacti, this way the bottom can pass nutrients to the top cactus (very important).
now take a tissue and fold it up into a square big enough to cover your peyote top. grab your electrical tape and tape over top of it while putting a little bit of pressure on the cacti (you want them to be firmly pressed together, no air inside). i put 2 pieces of tape over the top going in different directions, making a plus sign if viewed from above. now wrap some tape around the cactus stock where the tape from above is. this will stop it from unsticking or sliding around. place it somewhere in medium light (i use flouros) and high humidity. fungus can be a problem so keep up a good air flow. i keep mine around 70% humidity for one week. if the cactus tissue appears well healed and dry carefully remove the tape and very slowly acclimate it to outside (i take 1 month to do so).
have fun, it's pretty easy once you understand the principles of it.
happy growing
