Hi! Thought I'd chime in - hopefully this is helpful. Sorry it's long.
My (now) husband is a Peruvian citizen, but was on a 2-year work permit in Spain when we applied for his K1 visa. We went through the whole process in Spain and it wasn't an issue at all (I don't even remember ever being asked about his residency status in Spain). So a work permit should count as residency, even if it is only for a year -- just expect that you may need to be able to renew that permit in case the backlog makes the wait really long. (Example - We applied for K1 in August of 2020 and due to the pandemic backlog didn't get the interview in at the consulate in Spain until August 2021 - a year of time rather than the pre-pandemic expected 5-7months.)
I've also seen people go through this process while on student visas. I'm guessing it would also be okay on other visas that are not tourist visas or extended tourist visas.
For example, Spain has a visa type that is basically "I have enough money in my bank account that I want to come and live in Spain for a year -- I won't work or study, I will just spend my money and live in Spain." It's called a Non-Lucrative Visa. Before deciding to live together in the US, we looked at what it would take to get me (US citizen) permanently in Spain --- this Non-Lucrative Visa was an option that would have counted towards years legally lived in Spain, which would have counted as years towards getting Spanish citizenship. Since that visa type would have been considered "resident of Spain" enough to count towards citizenship there, I'd say it would have been good enough to count for residency for a US K1 or CR1 visa application. So something like that could be an option for her, I've seen it offered in other countries too.
From what I've seen, having a visa good for at least a year counts as you residing legally in that country (I wouldn't risk anything under a year). In fact, once you are on any of those visas in Spain (even a year long student visa), you are required by law to apply for Empadronmiento, which is legally registering the address that you live at with the Spanish government -- so if you are looking at the Netherlands, or any other country, see if they have something similar - she'll for sure be considered enough of a resident if she has a document like that. To clarify, I've been using Spain as an example, just to give an idea of what you can be looking for in other countries.
In short, my recommendation: Get a work permit, student visa, non-lucrative visa, or something similar in a third party country - she shouldn't have a problem with those. Just don't send her somewhere on a tourist visa and have her renew it a bunch of times, that won't count as residency.
Hope that helped and wishing you both all the best!!
PS - We have lawyers and prior to doing the K1 visa, they recommended we meet up and get married in Turkey (due to the travel restrictions of summer 2020, and me being a US citizen and him a Schengen resident) - they had multiple clients that had done that in order to apply for CR1. We didn't do it because there were too many risks involved at the time. Mentioning because Turkey could be a good marriage destination option that it sounds like you're already considering. There are multiple companies that specifically help foreigners get legally married there.