Was that sheer luck, or are there tips you can share to help expedite the process?

Pure luck. Some people don't get an AIMA appointment with their visa at all, and they are thrown into the hell of endlessly calling and emailing (and occasionally, suing) AIMA to get an appointment. Some people get an appointment but it's at the other end of the country (admittedly not a huge country, but still an overnight trip). After you get the card you have to renew in 2 years and again in 3 before being eligible for citizenship, so one time lucky means nothing. The biggest drawback of not having it (that I'm aware of) is that without the residency card, you are extremely limited in travel outside Portugal (one exit / entry, after your initial arrival) and still fall under the 90-day Schengen stay limit when in other Schengen-zone countries.

I don't think any of the immigration lawyers have any "inside contacts" of value(*). AIMA is a big, bureaucratic organization that appears to be dramatically underfunded / understaffed for the work they're doing. I expect we'll see similar results with US government agencies going forward once they discover that "AI" cannot, in fact, replace all the people they fired or the budget cuts they endured.

(*) Which said I don't really regret hiring a lawyer to help with NIF / bank account / VFS visa submission appointment prep / lease review / other delimited tasks. She was cheap on the scale of overall cost of getting to Lisbon, and gives some additional confidence. Others happily do it entirely on their own.