Side note for others: from what we can see/tell here, the vast majority of those having much longer processing times are PRs who are not in compliance with the residency obligation, and/or indeed not residing in Canada, sometimes for many years. Those PRTD applications need a positive H&C decision to be adjudicated. That's what takes very long - for the most part.
The problem is the uncertainty, but it's much less for those who are (well and clearly) in compliance with the residency obligation.
As you say, the issue here is the uncertainty. Publishing processing times for folks where "an instant and positive determination of compliance with the residency obligation can be determined" for each consulate would go a long way to help with this.
but there have been reports (eg in UK) of them being done 'quickly.' No, I can't say for certain how long; but I do recall having seen one done in about a week.
(I believe you can file for the PRTD before you leave for the UK, but I'm not certain).
A quick check suggests that might indeed be the case.
Other websites do say you should be outside of Canada when you apply, e.g
https://total.law/blog/permanent-resident-travel-document/ and
https://www.canadim.com/immigrate/canada-permanent-residence/travel-document/ - however, if one checks the guide at
https://www.canada.ca/en/immigration-refugees-citizenship/services/new-immigrants/pr-travel-document/how-to-apply.html for the United Kingdom it says it's possible to submit the application online.
Meaning that OP might be able to get a head start on the PRTD process before leaving on Thursday. OP didn't say how long the duration of the stay in the UK would be but if OP can get it done today and the trip is at least few weeks long, I think in that case the OP stands a good chance of having the PRTD approved before flying back. (But don't quote me on that.)
Getting a PRTD replaced in a single day is not realistic,
Fair. Even the US passport took something like a week to replace, though part of that was due to distance from the vacation spot and needing to travel to the embassy.
That said, for UK passport (and other visa waiver/ETA passport holders) it is generally far easier to travel to a US border town and cross by car/on foot. At minimum it's to your great advantage to have that option, from which many others do not benefit.
Yep, or if you have a B1/B2 visa for the US (a lot of Chinese and Indian nationals get these fairly easily after obtaining the Canadian PR card), then this option still works. (Though for the visa case, it perhaps is less helpful if along with your PR card, you also lose your passport at the same time...)
Worth noting though that not everyone can do this as even with the right passport you still need to qualify for the visa wavier/ETA. I knew someone from the UK (holding that passport) who was planning a trip to the US. It seems that this person had the unfortunate luck to have a panic attack during a routine police stop, and even worse luck when the copper decided to make an arrest. I heard that the judge basically tossed the whole thing out saying that the arrest shouldn't even have happened. Even so, this person had to cancel the trip to the US.
The person wasn't eligible for the visa wavier/ETA anymore - because of that arrest - and was required to apply for a visa at the embassy and discuss the circumstances with a visa officer. (In theory the trip could have gone forward after that - just the timing of the trip (and needing to return to work afterwards), the late discovery of the requirement, and the embassy not having open slots for an interview meant that the actual visa couldn't have arrived on time.)