Passport processing in a visa application center in a different country, when opted in for "Keep my passport"

I'm trying to help my fiancee plan a trip which involves two different kinds of visas for two different countries, one of which is the UK. I found about the "Keep My Passport" option:

Unfortunately, they don't describe what they exactly mean with "send your passport to TLScontact", is it any TLScontact centre in any country for which "Keep my passport" is also offered? or only the one in the country in which the application had been originally made?

This is quite important, because some visa applications take a long time to process, and if it would be approved while in the middle of the second trip, being able to fly directly from the second country to the UK could save quite a lot of hassle and money.

The "Learn more" button doesn't help, but they mention that the passport could be sent by certified mail (and thus possibly from abroad?). There are other questions about this service, but they don't cover this detail:

Keep your passport option when applying for UK visa

This other question instead provides an useful detail

I received a non straightforward email regarding my UK Visa application

The communication from the visa centre apparently said (2 years ago, at least):

Please submit your passport to the Visa Application Centre where you made your application within 28 working days from the date of this email.

So, I'm thinking of three different options:

1. Reach out to the embassy/visa application centre in the second country. Even if it's not clearly documented anywhere, maybe they could help, and accept to receive the passport there and complete the application there.
2. Once we receive an email which asks for the passport (presumably they don't ask for it if the visa application wouldn't be successful), just do the whole visa application again while in the second country (I understand that there cannot be two visa applications ongoing at the same time, and thus the first one would be cancelled, but at least knowing that it was initially successful would provide some reassurance in making plans). This makes a lot of sense since it's vastly cheaper to apply again for this kind of visa, instead of flying back to the original country and then to Europe+UK again. Though I'm not sure if it will be possible, to apply for a visa in a country in which one does not have right to abode (we can probably address that, but we obviously need to plan in advance)
3. Give up, and return to the original country (it currently takes 20 hours with multiple layovers, so it's definitely doable, but annoying)