This is what I found as to the measurements.
Seems to me, the 6.5x57 is the normal 57mm case. If brass could be formed from 6.5x57, ANY 57mm case could be used such as the 6mm Rem. & .257 Roberts, as well as longer 62 and 63mm, standard cases, like .30/06, .270 Win, .280 Rem.
If the measurements below are correct, the 6.5x54 case is smaller than the standard Mauser case of 57mm., which is why any of the 6.5's or .260 dies will work to neck size the 54mm. brass.

Parent case 6.5×53mmR
Case type Rimless, bottleneck
Bullet diameter .264 in (6.7 mm)
Neck diameter .295 in (7.5 mm)
Shoulder diameter .428 in (10.9 mm)
Base diameter .452 in (11.5 mm)
Rim diameter .454 in (11.5 mm)
Case length 2.11 in (54 mm)
Overall length 3.00 in (76 mm)
Case capacity 44.5 gr H2O (2.88 cm3)
Rifling twist 1 in 9"
Primer type Large Rifle
Maximum pressure (C.I.P.) 365.0 MPa (52,939 psi) [1]