Portugal Golden Visa seems way more succesful than its Spanish counterpart, not sure whether it is only because of the better tax treatment or also easier formalities. In Spain, Madrid and Barcelona appear to be more complicated than other areas.
I´ve used a lawyer for a couple of things, including tax advice, emailed the law firm yesterday about the appointment issue but didn´t get a reply yet, I doubt they can get it any faster.
Fwiw I`ve also tried a gestor , who are professionals, sometimes also CPAs, who help one to navigate he Spanish administration, she claimed she could get me a short cut for some procedure, but all she managed to do was having me to wake up very early, meet her up at the local tax department, for the staff there to tell us what she had in mind wasn´t possible. There are other disgruntled testimonies about gestors and law firms, reading Blueraincap posts I doubt he will be able to share the name of a company which is particularly successful. But I´d sure go the lawyer way if a reputable name comes up.
For some reason there is a bit more info online about immigration lawyers in Barcelona than Madrid.
Also fwiw, and no idea how the situation is in Portugal, we know a couple in the exact same situation as us : same nationalities, husband self employed (I registered as such just to get the public health insurance for the family, private insurance is very cheap and so far so good but it has way more limitations than public insurance, hence we do need both), and we are all moving from the same city in China. They probably arrived early July, and haven´t been able yet to get internet in the house nor to buy a car. Not clear whether they managed to get a bank account, without the lawyer intervention, coming from China, I´d possibly still be without one) They paid a lawyer in Barcelona who promised to get them the residence permits within 10 working days, which sounds difficult for the Mrs, I´m curious to see how it goes.
Good luck in Portugal btw, very relaxed country, I chose Spain because of a better sports school for daughter and me speaking better Spanish than Portuguese, but if not concerned about those issues, would have considered Portugal very seriously.
Again, the major issue of lack of available appointment only applies to non EU citizens, and possibly only in Barcelona and Madrid, I suspect if the same issue appeared for EU citizens, who are catered to in a different office, Brussels would be all over Madrid.