I think this is a good question, especially for the countless K users who have complained about cut K, and I wish it would get discussed by the RC users too, since the technology is within everyone's reach. Ketamine is a good candidate for recrystallization because it (the hydrochloride anyway) seems to be very stable. I admit I haven't tried to recrystallize K, nor have I researched its recrystallization, but I have lots of experience with recrystallization in general. For recrystallizing K, I would keep it as the hydrochloride first of all, for both convenience and because it is known to be very stable, and try recrystallizing it from alcohol, which is a good general polar solvent to try. Although alcohol completely free of water is ideal, 95% ethyl alcohol or 91% isopropyl alcohol will usually suffice. If you can, get a small borosilicate (Pyrex) Erlenmeyer flask, maybe off ebay, which is ideal for recrystallizations. While frequently swirling the contents of the flask, heat the ketamine hydrochloride with the alcohol on an electric hot plate, just enough so it simmers, and add little bits of alcohol over time until there is enough to dissolve all the ketamine. Hopefully everything will dissolve. If there is something like table salt present, which will never dissolve, then the solution will have to be poured away from the solid impurity into another flask. Then allow the solution to cool, slowly. After a day, you might be able to increase the amount of crystals by cooling the flask further in a refrigerator or freezer. Once it has sat several hours, pour the solvent into a glass or ceramic bowl to evaporate (or suck it out carefully with a pipette) and leave the flask on its side to dry before scraping out the crystals.
That's pretty much how it works. One nice thing is that, if your compound is stable like it is in this case, you don't really lose any of it (assuming you don't have any "accidents") because it will end up either as the crystals in the flask or as the residue in the bowl after the solvent evaporates. By comparing the color and quality of the residue with the crystals, you can get an idea of the purity of what you started with. If you started with completely pure K, then the crystals and the residue should be identical, except maybe in crystal size.
You may ask, if this is as good as recrystallizing the base, then why do the synthetic procedures use the base? Possible reasons are: the final product from the synthesis may appear as the base, so there is no inconvenience in starting with that form, or that there is only one procedure, copied and reused around the net, and the recrystallization was only experimented with once, so there was no optimization, or maybe recrystallizing the base really is more efficient, either giving greater separation of ketamine from impurities or a larger proportion of the initial ketamine in the final crystals.