The Portugese 1904's (or the 1904/39's) aren't actually "Mausers" - they are Vergueiro's.
The rifle was designed by a Port. military officer, with the bolt more Mannlicher then anything else.
The bolt of the Mannlicher-Schonauer was used as a basis, by Captain Vergueiro, for developing his action (derived from the Steyr Mannlicher).
Vergueiro worked with DWM engineers on the final details of his design (the magazine, barrel bands, sights, bolt release, ejector and bayonet lug are Mauser based).
Vergueiro's design was done to get around paying royalties to the foreign patent holders of the Mannlicher Schonauer and Mauser designs - they must have been treading a fine line there.
The split bridge action is certainly not up to the calesthentics of any cartridge based upon the 30-06 case - as IIRC the original chambering was the old 6.5x58P , upgraded in 1939 (Model 1904/30) to 8x57 (7.92mm)
It "might" make up into a nice 7x57 or 8x57 sporter, though - since they operate pretty smoothly, and neither cartridge is a bad choice with proper bullets.
.