You could politely reiterate to your boss how much this bothers you. "Seeming rude" is often in our own perception.

Hey, Boss, got a second? I love that we have a weekly meeting to hear from each other, and I'm worried I'm not able to engage fully because I can't hear what people are saying when they chew and talk. I know we talked about this in passing, but I've come to realize it's really limiting my effectiveness. Is there anything we can do about it?

You seem to have ruled that out, though. So then, I suggest both the following--but only if done in chronological order.

Next-best ideas

1. Even if your boss isn't receptive to your suggestions, try talking to a couple of your colleagues--probably the ones you're on best terms with--to get their assessment of the situation. If they agree with you, you have allies to change the culture of this meeting. If they don't, at least they know it bothers you. Assuming good faith, they'll still make a bit more effort not to do it when you're in the conversation.

2. If the talking and chewing is impeding your ability to understand important information from your colleagues, you should not feel shy about asking them to repeat themselves. Don't do this to the point of being obnoxious! The tone you use to do it matters a lot. A gentle, "I'm sorry, I didn't catch that," once or twice per meeting suffices.

The second point may seem like a passive-aggressive solution. Passive-aggressiveness isn't very good as a default mode; typically it impedes important communication and leads to a guessing game. In this case you've already talked to your boss and to a couple of colleagues, so you're not using this as your Plan A. Moreover, you do have a right to ask about info germane to your job. Encouraging them to change their behavior is a nice spillover benefit, but you need to hear important info even if they never change their behavior.

Again, don't overdo this (e.g. 3 or more times in an hour meeting), or you really will become a villain.

Best solution: Talk to your boss

You should politely reiterate to your boss how much this bothers you. "Seeming rude" is often in our own perception.

Hey, Boss, got a second? I love that we have a weekly meeting to hear from each other, and I'm worried I'm not able to engage fully because I can't hear what people are saying when they chew and talk. Not just that, but I'm really sensitive to noise. I know we talked about this in passing, and since then I've come to realize it's really hindering me from participating. Is there anything we can do about it?

You seem to have ruled that out, though. So then, I suggest both the following--but only if done in chronological order.

Next-best ideas

1. Even if your boss isn't receptive to your suggestions, try talking to a couple of your colleagues--probably the ones you're on best terms with--to get their assessment of the situation. If they agree with you, you have allies to change the culture of this meeting. If they don't, at least they know it bothers you. Assuming good faith, they'll still make a bit more effort not to do it when you're in the conversation.

2. If the talking and chewing is impeding your ability to understand important information from your colleagues, you should not feel shy about asking them to repeat themselves. Don't do this to the point of being obnoxious! The tone you use to do it matters a lot. A gentle, "I'm sorry, I didn't catch that," once or twice per meeting suffices.

The second point may seem like a passive-aggressive solution. Passive-aggressiveness isn't very good as a default mode; typically it impedes important communication and leads to a guessing game. In this case you've already talked to your boss and to a couple of colleagues, so you're not using this as your Plan A. Moreover, you do have a right to ask about info germane to your job. Encouraging them to change their behavior is a nice spillover benefit, but you need to hear important info even if they never change their behavior.

Again, don't overdo this (e.g. 3 or more times in an hour meeting), or you really will become a villain.