There is no way around it: if your team is top heavy there is no way to avoid high minutes unless you get garbage time at least once. Get the psychologist, a massage doctor, play strictly and off you go.
Great players don't start every other game
Exceptional players with shit conditioning can't play 30 minutes a night either...
Get backups with high ST and if you are adventurous (or have private league games) check what splits you get by starting the backups and using CPfDC