The dummy-pull is more about your leg and grip strength than upper-body. Grab a hold of the dummy with locked arms and a good lumbar-curve (your back posture) and drive with the legs.
Rather than going too crazy with gimmick-routines, you may want to train for the fit test. I am not saying that after hired there are better things to do, but you are just trying to get your strength up to pass the fit test. So, do lots of push-ups and do them often (every other day). Do them to failure and when you can't do any more, do controlled negatives.
There are several good techniques. You can use a deck of cards and work your way through it (and you are actually do small numbers of reps at a time (1-13).
Another favorite of mine is 30 seconds of work and 30 seconds of rest. Do 3 sets of widearms push-ups, 3 sets of standard push-ups, and 3 sets of diamond push-ups.
For your push-ups, do can start off elevating your upper body to get in a decent number of reps. Then slowly work yourself down to the horizontal on a floor.
If you have a bench press for the fit test, start working your weights. Do them with partners to reach fatigue. Shoot for a few sets of lower reps (4-6) vs high reps, as you are looking to increase strength more than endurance.
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