Let's say start is 9, 4:45 would be 7.75. 8 hour guarantee bumps you up .25, so there's most of your over allowed. They can't fault you for an under dispatch. Lunch doesn't count against production, so take it, it will help you rest up for the second half of the day so you can move more quickly. If you need to sort your car during lunch to qualify, no one ought to think less of you, just don't do it the whole time. Also, be at your next stop ready to deliver at the end of your lunch. This is actually company policy, according to my on road, so you won't get in trouble for driving during your lunch.
I felt like I had to run to qualify too, but once you get conditioned to the job, and get to know the routes inside and out, you will find that a slightly faster than normal walking pace will be enough. The time saved is all in the routines and automatic motions. When you aren't wasting time making decisions, your day gets much easier.