might suggest you check out Mike Dolce (of Dolce diet). He works with UFC as trainer/nutritionist.
So, I know for me, regardless of what exercise routine I'm doing (or not) ranging from P90X to Les Mills Combat to weight training to (in my opinion the best one for me) Krav Maga, I too can see the impacts around my middle depending on what I eat. Not as simple as carbs/rubbish or no carbs/rubbish but really, specific types of carbs even while keeping all other things the same.
If you're good with all the rest of you, maybe try a 30-day juice cleanse? BUT, doesn't mean 30 days of fruit juices, you'll need micronutrient rich drinks/smoothies (call it what you will). I have a MagicBullet aka Nutribullet that is fantastic. TONS of veg, dark leafy greens, some fruit, and pretty much whatever else you like from the complete nutrient list. 0 processed foods for 30 days. From pasta to potato chips. Avoid wheat and dairy (dunno if you're vegan or vegetarian). Get creative with things like ground flaxseeds, powdered pea protein (NOW makes a good product I got from bodybuilding.com) and you can use some unexpected ingredients like avocado (protein and omega3s).
but maybe up your routine further still for 30 days. Add in a mid-day run?
Something I don't really subscribe to, but seems to make sense, is the premise that it isn't only what you eat, but when you eat. Ranges from don't eat anything after the sun's gone down to when to have your biggest meal of the day or to graze and have like 5 meals spreadout.
Mike Dolce at seminar I went to talked about general philosphy of eating, that being: "Eat for what you just did, or what you are going to do". Meaning, if you've just blasted your body with exercise, or are getting ready to later, you need to either replenish what you just burned so the body can repair/restore/rejuvenate or fuel up with appropriate balance of nutrients to fuel your workout (different depending on whether you're needing to fuel a 45-60min Insanity session (or as I've learned) fueled up for endurance work like 1.5 hour Krav Maga blowout).
Lastly, I don't believe counting calories or counting grams of fat or grams of carbs, but more about avoiding highly processed anything (to include highly processed veggie/vegan stuff like veggieburgers) if trying to get cut before your honeymoon. Focus on the nutrients, lots and lost of dark leafy greens, beans, fruits, etc. and of course water. You should have all the energy you need, feel satisfied and maybe see a difference?
I'm not a nutritionist, just a bit of a health nutter and have read and tried different combos of things that worked for me. I didn't have honeymoon to prep for but rather to get in best shape of my life as hit 45yrs and mission accomplished!! (and still in progress because it's a part of my lifestyle vs a diet or one-and-done thing for me).