For the ladders where I have that trouble I slow the pace, and the rest periods then lengthen in proportion (the iphone app does this for you automatically which is handy). Also limiting the maximum number of reps on your ladders might help, where I hit that limit initially as you describe I just made the ladders go up to 4 reps, which let me finish the 7.5 minutes. As it's the muscular endurance component of the program it is a challenge and gets easier as your form becomes more efficient and you build stamina. If it's still a struggle maybe start with the beginner program - going by the reviews some gym users feel the need to do this as it is demanding and they didn't have the foundation of fitness they thought (that's been my experience). His website has a forum that he answers questions in if that doesn't do the trick.
For rest days I go by how my muscles feel and it varies, but I often do 2 days on and 2 days off so the week's workouts take me 8 days. As consecutive workouts target different areas and the sessions aren't all that long I think there's less scope for overtraining than there could be, so perhaps I ought to push it more.