I've gotten rid of several villagers without time traveling and its actually pretty easy. The first thing you must do is wait until someone (any villager) wants to move. Generally villagers will ask to move out after about 10-15 days after the last move out, so if you don't want to TT, you will have to wait that long. You will see the thought bubble over their head, and when you talk to them you can confirm that they indeed are asking to move. The next step is to
not answer yes or no, and instead turn the game off. Do not talk to the villager the rest of the day, and tomorrow the thought bubble will most likely be passed to someone else. Keep repeating this process until it lands on the villager you want to move. (Sometimes it might be the same villager for 2-3 days in a row. this can happen, just keep going!)
In regards to friendship points, I have had success with this method with villagers who I was close with and not close with. In my experience, friendship points did not matter, and I actually found that the villagers who I was not close with at all (recent move ins, villagers I tried to ignore) asked to move the most when doing this method. Lmk how it goes and if you have any questions!