Hello Lourenço,
I may be a bit late to the party, but will respond anyway, in case it helps someone else.
I would recommend a couple of things for people in situations like yours:
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If you do not have a PT immigration lawyer, you should likely get one as they can help smooth out the 10 day requirement - they know how to talk with SEF to get you more time and also to help you get the papers into SEF. If you do not have one already, I am happy to send you contact information for ours. She’s awesome.
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Go to a local police station (if possible) and ask if they can do official fingerprints for you. You are allowed to do them yourself on regular paper, but the FBI is quite picky about the prints and may reject you, and you have to start the entire criminal record process all over again (meaning, pay for a new report, and lose a lot of time on the clock).
If you have to do them yourself, I recommend that you use fingerprint ink (maybe Amazon or the like can get you some quickly?) as regular old ink pad ink often times results in rejected prints.
Also if you have to do them yourself, take several sets and print on heavier paper (light cardstock). You can print the official form which you can download online at the FBI website (it can be printed in B&W). If you have a bad print on one copy, by sending multiple sets, the FBI can piece together enough prints for them to clear you and provide the report.
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Make sure you are using the online filing and request your results via secure email (do not ask for hard copy to be mailed or that will cause big delays). Once you have the response from them with your case number (takes less than 24 hours, often it can take as little as 1 hour to get this number) you would send the hard copy prints to the FBI via DHL, UPS, whatever.
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Once they receive the hard copy prints, assuming they are ok, they will usually get you the final report within 5 days. You will now need the apostille.
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To obtain the Apostille from DOS, we have successfully used Monument Visa Services - they are quite reasonable for the work that they do and are very fast (although the total time to process the Apostille is still in DOS’s hands).
With Monument, you are able to upload a PDF of your record record that you pulled form your secure email and handle everything online with them. They know exactly how to fill out the Apostille forms so they aren’t rejected, and will get the application request into DOS within 24 hours (often times the same day, depending on when you get the docs to them - they are on the east coast).
The great thing about Monument is that they also help coordinate getting your hard copies of the Apostille from DOS. This is important, because DOS will not send your Apostille internationally. It must be sent to a US address. If you are in Hong Kong, this means that Monument is able to receive your Apostille hard copies and then send them on to your lawyer in Portugal (or maybe directly to SEF? I have not done that personally, so you would have to ask them), for an extra fee (which is much cheaper than the pricing I got directly from a US shipper). They also now offer a scanning service for something like $5, so that you have a copy for your own records (you must send the originals to SEF).
We have used this process pain free both abroad and when in the US with great success. Hopefully this helps you and/or anyone else that may have this same issue.
Good luck!