It sounds like you have two problems: (1) your game with 6-8 players has slow combats unless you use a small number of monsters, and (2) if you use a small number of monsters, your crowd-controllers can shut the encounter down.
The first problem is easier to fix:
- Use a larger number of monsters, but make most of them them identical so that you can run turns for them quickly. Move them all on the same initiative. "Okay, these three orcs are attacking you. Each of them makes one attack, with an attack bonus of +4... (rolls) they hit AC 11, 15, and 17. How many hits? Okay, take... (rolls) 12 damage." Optionally include one or two bigger monsters so that your crowd-controllers have something awesome to do.
- Consider splitting your game into two smaller games. You can start slowly -- have occasional "side missions" which don't involve the whole group. These will be easier to schedule: choose the time and place that work best for you, and see if around half of your players are able to be there. If that seems to work, you can have more and more side missions, and save the "full group" scenarios for boss fights and special occasions. In the extreme case, this turns into a West Marches scenario.
For the second problem: remember that D&D 5e is balanced around having a lot of encounters per day. Are you doing that? If you're only giving them one big fight in between rests, your characters with daily powers will be much more powerful than the designers intended, because they can use all their dailies in that encounter. Those crowd-control abilities: are they daily powers?
If you suddenly change your game from one fight per day to three or four, make sure to telegraph that in advance so your casters don't waste all their spells on the first fight.
One final note: it can be dangerous to have battles with a small number of active monsters. What tends to happen is each monster stands in one place and focuses all its damage on one player character. This is really bad for that player character, and it's sort of boring for all the other characters who never get attacked. One solution I've used for this problem is, when I have an encounter with just one monster, I make sure that all its attacks are area-effect attacks, so that it spreads out the damage more evenly. This involves a lot of inventing homebrew monsters, though, so it may not be best for every group.
Rules as written, it is left to DM or the table for interpretation
Rules as written what you're supposed to do is look at Nondetection and Portent and decide for your table how it works. You're supposed to look at what the intent of Nondetection and the intent of Portent is supposed to be, which means you'll have to read and decide for yourself based on how you understand the rules and what works best for the fun and enjoyment of your table. That is 5e's rules philosophy.
I don't buy the "It doesn't say it is or it isn't, therefore it isn't." You can just as easily say, "It doesn't say it is or it isn't, therefore it is." Lack of evidence doesn't prove anything. The game rules do not claim to be comprehensive, and this is the natural consequence of that. This is the entire point the "rulings not rules" idiom is making. There is no burden of proof on Portent or Nondetection or the PHB as a whole to provide an answer. While that line of reasoning was implicit to 3e and 4e -- both editions that sought comprehensive and complete rules sets -- 5e actively does not do that. 5e D&D is often intentionally vague so as to leave rules open for interpretation and the system intentionally doesn't use keywords or raw mechanics. It does this so that players and DMs have the explicit freedom to interpret the rules for themselves and do what makes sense for that interaction. The designers know they can't possibly foresee every interaction in the rules, so they no longer try.
There is no clear answer by design. Yes, this means that asking, "What is RAW?" on RPG SE for 5e D&D is often a pointless exercise because the answer you should often get is, "RAW it depends on your table." This is why there are so many conflicting answers on RPG SE for 5e questions and why Sage Advice contradicts itself so often.
The rules are less important than the game. What Mearls and Crawford want is for players and DMs to stop asking WotC how to play and just make a decisions and play for themselves. If you make a mistake, admit it and make a correction. It's no less destructive than doing nothing until WotC makes a decision and then maybe changes their mind later.
You're expected to look at whole picture that the rules are giving you and to make a judgement call on what feels the most consistent and correct for your table. Is it reasonable for Nondetection to block Portent? Sure, it almost certainly is divination magic given that it's an ability of the Diviner subclass. How about a Ranger's Primeval Awareness? Well, that works like a spell, even consuming a spell slot, and it would have to be divination magic given the distance, so sure. How about a Paladin's Divine Sense? Hm... possibly, it's pretty close to Detect Good and Evil, but it's really described as the Paladin's senses. A Warlock's Devil's Sight? Hrm, hard to say. It's got elements that only True Seeing can accomplish, and Nondetection probably blocks True Seeing, but it's basically an improved Darkvision spell and that's not even Divination. So maybe partially? A Barbarian's Feral Instinct? Eh, that doesn't seem right, it's not magical. A Rogue's Blindsense? Yeah, probably not unless Blindsense is supposed to be magical, but I don't get that impression.
Best Answer
With the Divination Wizard in my party, the basic idea has always been that the Wizard tells me beforehand if they want to mess with a roll.
This usually takes the form of "I'm going to cast this and replace their saving throw" or "If this guy attacks my Rogue buddy, I'm failing his roll" and if none of those things happen, I just roll as usual.
I always make sure to include enough story and description to give players an idea of what's going to happen and give them a moment to interrupt.
So if the evil advisor to the king is about to deceive him into getting the party thrown into jail, I will first say "The advisor bends over to the king and whispers things in his ear while giving you the evil eye" and then wait a second or two and if nobody reacts with "I'm interrupting this" then I make the roll, whatever it is. Could be a Deception, could be a Saving Throw for the king, depends on what happens.
But the players will know what in-game fiction they can interrupt and if the Wizard asks "what kind of roll is this? I might want to change it", then I tell them, and they can decide to apply portent.
This shouldn't come up as often as you think. A portent can only be applied when you can see the target, and generally when you see them you'll be aware of what they're doing. In the few exceptions, I'd call it out beforehand.