Ah okay this flicking between doesn't seem so odd now when you put it like that. The only place where it is still disturbing is here:

- Сейчас я смотрю футбол, а вечером буду писать курсовую работу. Кстати, Восток - Запад я уже посмотрел.
- А когда ты его смотрел?

Now I get that you have stated in this case for some reason the experiential perfect with this verb can be expressed by both (he has watched it, the experience lives with him, but he isn't denoting that he completed it recently... which would lead me to use the imperfective)

So what I know... In Wallace and Gromit when they are on the moon, and they taste some cheese he says "This isn't like any cheese i've ever tasted" and uses imperfective пробовал (then immediately after says perfective попробуем.. to mean let's go try some other cheeses)!
-Dave Chappelle in a sketch is being stopped by the police and asks if the police officer has his show using imperfective видел.
Many other examples have happened today while chatting on VK which make sense to me and correspond with this experiential perfect.

I get ALL of this, it makes sense, imperfective for experiential perfects (have you evers) and perfective for the standard completed action (simple past, resultative perfect etc...). The crossover doesn't bother me so much if you tell me this is just how смотреть is... what bothers me is that one person stated already я посмотрел (perfective) and then the other person replies... NOT using the perfective??? That seems just weird to me but if it's something I have to accept I guess I just have to accept it. Why would he not reply using the same verb form as the style and information the verb carries has aleady been dictated by the first speaker, I would have thought.

Would it be completely possible that both these sentences use the imperfective смотрел, as from what I understand so far that is what I would instinctively do.