I can offer a little bit of insight on this. I teach English to young Japanese kids, and in a recent lesson, we were comparing the sounds of the names of different English letters and grouping them according to which names had similar sounds. For example, out of the letters A, N, Y, D, K, P, I, H, M, T, the task was to recognize that D, P, T all ended with "ee" sound.
Of course, for Japanese people, this is actually represented with the hiragana い ... as a result, many of my students thought that it was odd not to include A, K, I and Y in that group, because in the Japanese way of thinking about their sounds, they all end in い as well.
When I played the names of A, K, and H together, though, students realized that they were a better "grouping" because they all contained the "ay" sound, which in Japanese would be represented with the hiragana えい.
Likewise I and Y "go together because they both have the sounds あい.
I only use this example to point out that Japanese people are very attuned to the a, i, u, e, o sounds, and can easily distinguish between an elongated ええ (ee) and a blended えい (ei). In Naruto's answer from the other Stack Exchange link you found, where he said that Japanese people would "sound out" the word sensei like this
せ、ん、せ、い。 （or せ、ん、せ、え。）
I am not sure that they really would use the second version... the combination of えい is not meant to elongate the え... when I ask my fellow teachers to sound out words containing えい like sensei, they have always used せ、ん、せ、い, and not せ、ん、せ、え. The sound is noticeably different. "Relaxed" speech might produce a sound closer to せんせ without the い sound at the end, but that's not an acknowledgement of a deliberate elongation of え, that's just casual speech.
This reddit conversation follows a similar line of questioning, and might be useful:
おう on the other hand, is a different case. A う following a kana ending with an お sound elongates the お sound. う is a "weaker" sound than お, and becomes subsumed in it. When "saying it out slowly" however, Japanese people are likely to enunciate the う sound as "oo", mainly to clarify which kana to write down, not to imply that that is the proper pronunciation. This is because おお combinations also exist.
to sum up, えい sound combinations are NOT meant to elongate the え sound, and Japanese people are very aware of and can clearly hear the two separate sounds, while おう sound combinations ARE meant to elongate the お sound, and Japanese people recognize this elongation, and PROBABLY do not usually enunciate or clearly hear the う within the long sound.
The one exception for this is when the う sound following the お sound is not part of the same kanji the お sound is part of. As Eiríkr Útlendi mentioned in the comments, verbs ending in う with a preceding お sound will clearly pronounce the う, and this is because the う is the part of the word that identifies which type of verb it is, and which ends up being conjugated. Also, words consisting of multiple kanji, where one ends in お and the next starts with う, will follow this rule as well. Where there are both in a single kanji, however, the "elongated お" sound is the rule.