Those are in fact the standard ways I was taught, in an English-speaking Latin class, to pronounce short i ("hit") and long i ("heat"). But that isn't necessarily historically accurate.
It's definitely worth noting here that the english words "hit" and "heat" are felt by native speakers to use two different vowels (referred to as "vowel quality"), whereas the Latin "occido" and "occido" were felt to use the same vowel, in different lengths (referred to, oddly enough, as "vowel length"). That's why they're spelled the same.
Similarly, Japanese kana don't have different symbols for the short and long versions of their various vowels. Long vowels use the symbol for a short vowel, followed by a length mark.
English does use differing vowel lengths, but english vowel length is fully determined by other things; it doesn't vary freely. A standard example would be that the vowel in "made" is longer than the vowel in "mate".
The "long" and "short" used in English classes (not Linguistics) usually refers to the presence of a "silent e" and the lack of "silent e", but this terminology does not necessarily match up to a phonetic long and short vowel.
I remember hearing an argument in a linguistics class that for English oral stop consonants ("p","b","t","d","k" and "g" at the end of a syllable), the primary source of differentiation between minimal pairs, like "made" and "mate", is vowel length and that they are all devoiced.
I'm aware of the English-class terminology, but interestingly enough the guy bringing up "hit" and "heat" wasn't using that, as "heat" would be described under that system as having a long E, not a long I.
It's definitely plausible to me that (when the word is pronounced in isolation) word-final stop consonants are all devoiced. I haven't looked into the question at all and don't plan to, so I'm basically just spitballing. But my vocal tract can definitely start running down before I entirely finish speaking.
However, a much bigger issue than distinguishing "hid" from "hit" is distinguishing "hip" (where the final stop has become a glottal stop) from "hit" (ditto). I was under the impression that in general there isn't necessarily any phonetic difference at all there. If the argument you mention was only referring to minimal pairs with the same place of articulation, that sounds more reasonable.
I think final glottalization is a definite possibility, but I don't think it is a huge issue for native speakers given that context and word usage will resolve it for the most part.
្The /I/ in "hit" and the /i/ in "heat" are two different vowels.
When linguists say that a language has minimally contrastive vowel length, they mean that a single vowel can be pronounced with either a short or long duration, resulting in totally different words.
So in Khmer...
យឹត /jɨt/ means "to scold"
and
យឺត /jɨɨt/ means "slow"
A long vowel is indicated typically in the IPA either by doubling the vowel symbol as I did above or by placing a macron on the vowel (a line over the top, as in /ā/).
As was mentioned, the terms "long vowel" and "short vowel" learned in English class are misleading and bear no reality to the duration of English vowels.
