It doesn't sound as though you're particularly sweating the pushups nor the situps (nor should a man who has reached the "Simple" goals be worried about them, either). As Mr. Fox has already stated, the ten pounds comes down to the kitchen more than the gym. Just do yourself a favor and however you tackle the weight issue, do it in a way that you can maintain once this test is over--as a Navy Command Fitness leader, I can't begin to express my frustration with certain folks when we end up doing the same dance every semi-annual PFT cycle... The crash diets, followed by the ballooning weight immediately after and the accompanying complacency of having six more months before they have to worry about it again.
That said, if you have the conditioning established for it, I would recommend Dan John's 10,000 swings in a month program: https://www.t-nation.com/workouts/10000-swing-kettlebell-workout . This is one that I subject my students to once they've built up the work capacity to handle it (for me, when they're doing 300 two-handed swings daily in 15 minutes or less with 24k for men and 16k for ladies and are fully recovered before the next workout). It's never let me down, and I can tell you that one completely de-trained male student of mine dropped from 23% bodyfat to 19% as per the notorious "rope & choke", as well as dropping two pants sizes from the experience. He also performed the best PFT he's had in years.
Many ways to skin the cat, though. But I personally feel that you can't go wrong with the simplicity of this one.