Minimizing fueled mass of the vehicle is a stupid thing to do. It's optimizing the wrong metric.
Scramjets also suffer from bad thrust/mass and thrust/$ ratios compared to rocket engines.
Overall scramjet launch vehicles are an example of pyrrhic engineering: even if one could make such a vehicle "work", no one would want it.
Scramjet launchers (and air breathing launchers in general) have been looked at extensively, for decades. They don't make any sense. The math just doesn't work. Here's an insightful post from the Old Usenet that illustrates the difficulty:
https://web.archive.org/web/20220131115058/http://www.island...
When reading that, remember that LOX is 20x the density of LH2 (or 17x the density of "slush hydrogen").
"Rockets, not air-breathing planes, will be tomorrow's spaceships"
(New Scientist, 2009)
https://web.archive.org/web/20101017031109/https://www.newsc...