Some quick thoughts...
Idea for 3R's in Amend & Clarify - I wouldn't know how to put this into 3 R's (and I don't think a rule would really help anyway), so instead I would absolutely let the proposer take as much time they need, and they don't even need to be talking about the proposal (you don't need to be interpreting their comments). Afterall, they didn't get a reaction, so this is kinda like their reaction space. They shouldn't ever feel rushed or unprotected.
With that said, IMO the best way to handle consensus-seeking, or objection-avoiding amendments is to remind the proposer, "Remember, no one is allowed to help you here, but that's Ok because you don't need it at this step. If people feel tension about the proposal, they'll raise an objection." Or "Remember, we just want to make sure what we have would solve YOUR tension...we may need to come up with something else, but you shouldn't worry about that at this point..." Ideally, the proposer is given clear and supportive direction about how to navigate that step. Don't assume they know what to do, and definitely don't ever convey that they're doing something wrong (it's just not helpful when compared with telling them not to worry, and equally important, WHY they shouldn't worry; i.e. "We want people to raise objections.").
Testing the Validity of a Proposal - Kinda unspecified, but in my experience, it's usually best to do the testing in Clarifying Questions. Just as any other clarifying question. If I get enough data to turn my yellow flag to red, then I take a timeout to explain the rule and give them another chance to help me understand. I've only ever had one case when it actually wasn't valid, and in that situation, once I explained the rule, they immediately got it and dropped the agenda item. The big mistake here is to mistake a proposer's inability to articulate the issue according to Holacracy-type language and expectations as not being a valid tension. Especially people who aren't used to having to provide their reasoning. In my experience, just as a human person, I don't always know why I do what I do. So, cut them some slack and help them translate what they are sensing. Truly invalid proposals are usually identifiable because the proposer has a certain lightness and carefree-ness to what they are proposing, which only makes sense because they're not actually feeling tension about something, they just think "this would be a cool idea." This is a pretty serious topic in my mind, because a lot of damage can be done if people feel like there is a high-bar for governance proposals.
what do if someone "sneaks" another Tension during Integration round - Yeah this is a great one! So, the right thing to do is ask the proposer..."Does this change here [be very specific]...is that also a part of your original tension?" And I ask that question with genuine curiosity. Meaning, it's not a rhetorical question meant to embarrass them (i.e. I'm not thinking of them intentionally "sneaking" a tension in). It's possible the new bit actually IS part of the original tension, it just didn't get communicated earlier. When I've asked this I find people are pretty honest.
If they then say it's not, then you say [and be very confident and directive], "Ah! Ok then, then that's a separate agenda item...Secretary can you add that as an agenda item?...and we'll do that one next. So, Secretary remove that bit for now...." or something like that. The point is that you have an obligation to, 1) ask the clarifying question, and if it isn't, 2) process it separately.
Might that feel awkward? Absolutely. Afterall, everyone seemed OK with it. But again, everyone being OK with it isn't the criteria. The only way to really tell if it's part of the original tension or not is to ask the proposer. They are the only ones who can determine where the line is. The facilitator's job isn't to judge its veracity but to surface the information and move things along accordingly.
One final point on this because I really really really really appreciate how awkward this can be. So, if someone asks a timeout question like, "But wait...why in the world would we add a new agenda item when we're already here!?!?" then here is one effective way I've found to answer that question is something like:
"Yes, you know what, to be honest...in any given case it may be faster to just make that change now. But here's the thing...by using a defined process, we will absolutely move faster overall. It's like a traffic control system. Sure, in any given case, it would be faster for me to ignore the red light and drive right through the intersection...I can see no one is coming...it's probably safe...but as facilitator, I'm not in the position to make subjective judgments about what rules I personally think we should follow. So, we follow the process and the rules as defined, understanding that sure, in any given case it could have been faster to just integrate that bit, but that's a sacrifice we make to having a clear process that allows everyone to get where they are going as fast as possible. So, it sucks when I hit a redlight when no one else is coming the other way, but I understand that overall, stopping at redlights makes sense for everyone."
And I've actually said much more than this too! LOL. I just think it's such an important point to get across that it's worth taking some time for some discussion to address any people's reasonable skepticism that this process will "help them solve their problems more quickly."
[@mention:449411339497350002] and I have talked about this quite a bit and he has a really cool graphic that also makes the point really well. I would post it myself, but I don't know where he stored it. [@mention:449411339497350002] would you be willing to share it?