Well, it's actually HICONI (haiconi, to be precise, but you seem to know that "ai" makes an American English "i" sound as in "ice"). You don't need to drop the "i" in this instance because there is an actual kana symbol for "n." You just can't use it at the beginning of a word.
I'm not entirely sure what it means, but it looks like it might actually be two words shortened and smashed together. My first guess would be "High _______."
Also, it appears to be direction regarding the background, rather than the cels at all.
Maybe you can figure it out from there? If someone can translate the direction beneath (I probably could with a close-up of that first kanji) you might get a better idea of what haiconi means. The directions say "______ oneigaishimasu" . . . "Please ________." It's a little too small for me to count strokes or figure out radicals as it is. A native speaker probably could.

I tried, but my guesses went nowhere.