Scenario 1.

I'm in the UK on the SOR.

- On day one, I receive a replacement passport. That same day I declare to police that I'm leaving the country tomorrow
- On day two, I leave.

While I am abroad, the clock is paused on my 3-day obligation to report the new passport, has it not?
And the passport is clean everywhere...


Scenario 2.

I'm abroad, e.g. France

- I order a replacement passport while abroad.

While I am abroad, the clock is paused on my obligation to report the passport, has it not?
And the passport is clean everywhere...


Scenario 3.

Exactly the same as 2, but Gibraltar, and I there order the replacement passport from the office there, while still out from under the SOR registration requirements?

Until I return to the UK the passport is clean is it not?

There is no margins of grace. You have been prescribed the time limits and it is your responsibility to abide by them. If you don't, you will be in breach of your SOR notification requirements... you don't want to be in that situation.

If you are in doubt of any requirements you should contact your responsible police officer and get the response IN WRITING.

you have to give minimum 7 days notice before you travel. 

If you lost a passport and had to get an emergency replacement, it would probably be unwise not to email your PPU team with the new details. 

When you are abroad, you are under no obligation to report additional flights made before you return and don't have to give notice of them, although you might want to anyway so as to be seen to be honest. The passport itself contains no details of your record. The chip on the passport only contains digital versions of your photo, signature and personal details. Only UK passport control can see that you are subject to travel notifications, and not even see why (you might be a football hooligan, or a spy). Other passport control in other countries can't see anything about your record unless you have been flagged on interpol. You won't be flagged on interpol unless your crimes specifically involve travelling abroad to commit crimes or you've otherwise given police a reason to suspect you. Or if you've not declared your travel in advance properly.

For example, you go to Hong kong declaring a 180 days stay on your notification which is the max visa free stay for a Brit there. While there, you go to some other country at short notice. and another. and another. None of the intermediate flights need to be declared. No warning will be on interpol.

When you return to UK, passport control will ask if you if went anywhere else, and check the pages for stamps while you answer, so answer truthfully. If you didn't drop your PPU an email to tell them what other trips you made then you can expect them to call you to ask a few questions about what you were doing. But ultimately there's nothing they can do to stop you or penalise you, assuming you returned on time or otherwise emailed them to say your changed your return flight, if you also did that.

To be fair if you breach SOR admin requirements, the worst that will happen is you are taken to court and issued a fine.

P.S. you seem to be confusing SOR requirements and SOPO/SHAPO requirements. The latter is not enforceable when you are abroad. The former relates to how you leave and enter the UK and keep the police informed of your location so does still apply, it's not 'paused'.

I'm not seeking margins of grace. 

As I understand it, your obligations to the Register are paused when you're abroad, right? How could it be otherwise? Abroad there are no police stations therefore your non-notification is excusable.

Hence why bank cards that land on my doormat while I'm abroad don't get me in trouble. I just declare them within 3 days of getting back to the UK.

I'm not so sure about that!

There's something wrong with these two points of yours, in my experience of travel , and of talking to other ex-cons.

- I'm pretty sure even a domestic sex crime gets in the way of you entering the US, owing to interpol notifications.

- When returning to Glasgow airport from Berlin, I was asked no questions at all. Although I suppose there was nothing in my passport to prompt any questions, as I only took a detour into the Netherlands.

You should be because it's factual. Unless you repeatedly and blatantly do it of course.

On your first point, you might not get in, if you declare your convictions, and your PPU might not be keen on you going without being sure you got a genuine visa only because they know the americans will complain and get them in trouble if they find out. But it won't be because of any interpol notifications unless your PPU tell you they are putting one because you have genuine reason to give them concerns.

On the second point, if you've been in europe, they know everywhere you've been anyway, and the desk officer might not ask you anything if he's busy even if the 'ask more questions' flag is on. I've only ever been asked additional questions once on returning on over half a dozen trips, but a record of your return still goes on the system with any comments from the desk officer if they made any. But it's nothing to be worried about.