I'm pretty sure the tuning is the traditional G-D-A-E (double-octave violin).
The instrument (whose earliest mentions date back to the 1880s) was first used in the context of the local popular music orchestras called
tunas.
Joel Pina (1920-2021), originally a mandolin player, joined one around 1940, soon moving to the ABG (
viola-baixo, back then more often called
violão baixo) thanks to the zero need for adjustment to the tuning, and later (
ca1950) introduced it to
fado, where it hadn't been used before.
Here he is (barely visible behind comrades) in 1962 with his weapon of choice (
Preston tuners and all) :
Clearly, there are some players who still tune like he did, which I already suspected since the AGI/NOVAGI/Dragão string company, located in the Porto area, makes a string set for it, the D037:
http://www.novagi.pt/en/cordas-para-instrumentos-musicais
Nylon-core, silver-plated copper. In case anyone's interested, it is available here:
Dragão D037 Violã Baixo Acoustic bass Bass Classical 4 string
Your point about tuning higher very much stands.