Would you say I could "coin" the term "midnight-sunrise period" for a scientific publication?

If it's a science publication, I would go with that phrase. I looked up madrugada in the Portuguese Wikipedia.

Madrugada é o período do imediatamente anterior ao nascer do sol, sem horário pré-determinado.

It links to the English version's entry for dawn. Another dictionary I looked at, offered the English wee hours of the morning which is roughly what you want. For me, the wee hours of the morning includes not just the ttwilight of dawn but the dark hours before it.

Where's Anna when you need her? (She speaks Portuguese.)

Ceci n'est pas un seing.