Realistically, you can do whatever you want. Want to remove the conditioning, sure you can! Want to change jump training for squats, no problem! Want to pull out pull ups and instead do bicep curls, of course! Want to remove the Monday max effort day and swap it out for an hour in a cafe sipping a soy latte, all you bro!
Thing is, you do any of that, then you're not running DeFranco's program, and you lose the right to claim you are.
If you want to try to follow the program, then you follow the program, as written, exactly as written (barring any necessary modifications; I once trained alongside a guy who'd lost an arm, he couldn't do the standard bench press, so he used a single dumbbell. THAT is a necessary modification). Follow it for a good few months. I haven't read the whole article, so I don't know how long he suggests running it, but whatever he says, do it.
You want to become a better athlete? Awesome! What's your sport?
Looking at your lifting numbers, you need to get stronger. A lot stronger. Be consistent, and pretty much any program should get you stronger. Also, you don't mention deadlift numbers at all, you should be deadlifting.
Ideally, if you want to be a better athlete, you want a basic strength program you can follow 3 days a week, training that doesn't leave you too sore, then you do skill work for your sport the other 4 days.
If you don't have a specific sport, then just follow the program, exactly as written, for a decent period of time (at least 3 months, ideally 6+) and see how it works for you.
If you want a program more specific to you, then hire a good trainer to write one for you, otherwise, just follow the program and don't modify it.