I have no scientific data/resources to back this up; only personal experience between my hubby and me.
We've done the same thing you're doing, daily walking, no junk food, replace soda with water...we haven't reduced carbs, per se, but we incorporate healthy carbs into a more balanced diet than we had before. We started this last July.
Hubby was a beer drinker; I liked vodka and just about everything else under the sun
. We swapped all that for a nightly glass of wine (sometimes white; sometimes red -- never pink!!). It took some getting used to, but to be honest, eating "good" foods taste really good with different wines...so it wasn't too, too hard
. Plus it was a learning experience for us in addition to learning/trying new healthy foods, and now we have incentive to enjoy different restaurants that have a good wine list.
Anyway, we've successfully lost a good bit of weight (25 lbs or so for me; 30 or so for hubby). Could we have lost more without the nightly glass of wine? I don't know. I'm pretty happy with our losses up to date, and we didn't have to sacrifice our evening buzz.
I've always heard that rum is very high on the calories. If you just can't do wine no matter what, maybe a liquor that's a little more frugal on the calories?
Good luck & cheers