Thanks for the nice photo of the spiking phal keiki. It is a classic!
Years ago (early '90s), one of the San Diego phal growers gave me or sold me a small glass jar of what he called "keiki paste". I don't know if he made the stuff up himself or if he bought it somewhere. The glass container I got it in was unmarked.
He instructed me to smear a small bit of the paste on one or at most two of the previously-bloomed nodes on a phal spike to initiate keiki growth. I tried it on a number of plants just for the heck of it and got almost 100% success. Unfortunately, I let the keikis suck the life out of the mother plant (refer to Louis's photo above) and the mother plant either died or was set back for two years or so. These were adult plants blooming for only the second or third time but being greedy, I wanted lots of duplicates for trading with my friends. What I ended up with was a duplicate of my mother plant that took two years or so to bloom themselves...not a good "dead motherplant" tradeoff!
Later, I tried an experiment by putting the paste on a cut spike stuck in a glass of water. Guess what, it worked so-so. The keiki developed small roots then stopped growing. I harvested it and had a small duplicate of the mother plant without all the stress of the previous experiment.
Keiki paste is available on the market I see. I just did a "keiki paste" Google search and found sources and instructions. Your mileage may vary!