Oh, OK, I didn't mean to choose an example where the meaning changed.
In English, which doesn't have such a strong vowel length distinction, people say things like "u...um", "ye...ah", "ri...ight", etc., where the vowel is extended to arbitrary length. Are there similar cases in Japanese where a vowel can be extended for emphasis, hesitation etc., without actually making a difference to the meaning? If so, in those cases, do Japanese still mentally count "beats"?
I'm not sure if え...えと and あの...う might be examples in Japanese. Let's say they are. Then, I'm asking, for example, if Japanese speakers would always perceive that they were saying えと, ええと, えええと, etc., or whether in some cases they would perceive that they are just making a vowel sound of indeterminate length (and it doesn't matter).