I have been to the Oktoberfest only once and on a single day, the opening day, so this is not any exhaustive experience. I think it is pretty hard to give a precise answer to your question.
The sources you quoted sound realistic to me. The exact time to come is obviously unknown because every tent does not get filled at the same time, there are even multiple entrances to the tents, ... For the weekend, it changes everyday because the opening day and closing day are probably the busiest, and there are only 3 weekends, so only the middle weekend might be easier to get in.
Anyway, my memory was that getting in a tent just after the opening ceremony, around 11 AM (maybe later since tents start serving at noon) was not possible on the opening day. We managed to get in the late afternoon but I suppose it was pure luck.
On weekdays, German people likely meet at Biergartens in general just after work, sometimes as early as 4-5PM, so getting in before 3PM does sound reasonable.
In the end, to be honest, there is no set time the tents will have open spots or not. Given the popularity of the event, people there, including you, spent much money to even be in Munich and attend the event (and not only try beer), and you are likely to make the effort to arrive very early, wait if needed, and stay the whole day, or most of it. So get there as early as possible (in the morning on weekend days, in the early afternoon on weekdays), and once you have a spot, stay there, enjoy the beer and chicken.
Another way to make sure you can sit inside a tent would be to reserve your seat. You can still book your table for some tents, even though some are already full. Reserving a spot usually costs you to pre-buy 2 maß of beer (1 liter each) and food for each person on the party, but it is up to every tent to decide.