That particular sound I would call short I, though I admit there is no official name for the IPA I used earlier, which is a reduced short I. (Phonemically, all reduced vowels in English are schwas, as far as I know. But they are different phonetically.)
I have no problem with a patchwork. I think that’s better than creating new symbols that confuse people like IPA does. IPA is intimidating for people to learn, and most people can get on without it.
To me, the point of communication is to be understood. The long/short concept has a long history and people know it. It’s the way they were taught as children when learning to read, so it often communicates better than IPA. At least, amongst native English speakers. I realize that it screws up anyone who speaks a different language, and that it’s more phonemic than phonetic, due to pronunciation variations.
You also run into the problem of IPA having no real word for the concept when speaking, unless you go very technical and refer to the “near-close front unrounded vowel.” And, really, how close is near-close? And how unrounded is it? It’s not unrounded in choral singing, for example. And it sometimes drops to near- or mid-front.
The best you can get is to say the sound, which sounds incredibly awkward, and is very hard to isolate without accidentally adding another sound to it, like a glottal stop. The only other useful name I’ve seen for * is open I. But then, according to your logic, wouldn’t calling something open imply there are only 10 vowels, with open and close pairs?