Yes, the sugars need to go, and I would recommend cutting back on sweet potatoes to 1-2 a week!! I know this sounds hard, but u did ask and we are telling u!! I wouldn't cut the coconut water out, but have it after instead.
It is a very common misconception that we NEED carbs. This just isn't true. Our body will make glucose if it needs it, from other sources like protein. When you start to go low carb, u can feel pretty crummy, but if you up your fats and protein, in that order, it will largely help with the carb flu issues!! Start out slow, your body needs to adjust!! But sugar is not your friend, EVER. most people find that they lose the most amount of weight and it it is fat, not muscle, when in nutritional ketosis there is a whole boat load of info on that that is very worth reading, right here in the forum, sorry, don't have the link, but you can't miss it, it is usually at the top of the nutritional forum page!!
OP is already getting 50-60 g of carbs a day. How low do you suggest he go? Also, he is a 30-something male at 29% body fat. It is unlikely he needs to be that severe with his diet to get to his goal of 20% body fat.
I highly recommend Volker and Phinney's The Art and Science of Low Carb Performance. All your answers are in there. For short, I'd say ditch all sugar and high starch carb at once, focus on high fibre/low carb green veg, healthy fats and moderate protein.
Most of all, good luck!
OP: Fair warning, I am going to be the bearer of some sobering news.
I don't know how accurately you are tracking your process in terms of body weight, composition, and caloric intake, but given what you've told us, you are off in at least one of those metrics, possibly all of them.
If for a given caloric intake your body weight and relative fat mass are constant, then you are living the textbook definition of equilibrium. The only way to effect change while at equilibrium is to reduce energy supplies relative to maintenance levels to induce your metabolism to rely on its stored reserves, thereby converting mass into energy and getting you to a lower weight point.
Translation : You've got to eat less.
And there's the rub : less than what? I suspect that you probably don't have a good handle on how much it is that you are in fact eating. While you do provide a guesstimate of your daily caloric intake, there are a few telltale signs that you are approximating, and as a rule, people generally underestimate their food intake. You make reference to volumetric measurements of several quantities of calorically dense foods that you eat, specifically 1/3 cup of almonds, 1/4 cup of olive oil, and you provide no measures for the other foods you eat.
Action Item 1 - Do not use volumetric or portion measures to ascertain how much you eat, use a scale for mass measurement.
You will still be approximating your food intake even if you resort to mass measurement of everything. However, the goal here is to decrease the variance of our measured intake, not to measure perfectly, which is simply not possible.
Action Item 2 - Assiduously measure what it is fact that you are eating for several weeks during which you are weight stable.
You want to develop a reasonable baseline for how your metabolism responds to various caloric levels before starting to make changes.
Action Item 3 - Eat real food, but less of it.
This is the basic weightloss / recomposition strategy: you need to create an impetus for your metabolism to oxidize fat, and that is only going to happen in the face of an energy shortfall. Tactically, you can resort to various approaches, including ketogenic diets, or Otzi's all potato monstrosity among others. You need to be perfectly clear, howerver, that whatever you do will merely be a tactic in the overall strategy of creating an energy shortfall. Anyone that tells you that you can get away without being acutely aware of your caloric intake is woefully naive. Your choice of tactic will ultimately be dictated by which approach helps you to best control your appetite. I have personally applied intermittent fasting to great effect.
Anecdotally, we are both actually fairly similar in our gross statistics. I am, near as makes no difference, 6' tall, around 180 lbs, 45 years old and I'm sporting the lowest body fat percentage I've ever had in my life, somewhere in the high single digits. The only way I managed to get here was by very carefully controlling what I ate, and to break through the double digit body fat percentage plateau required me to eat around 1500 kcal. per day for several weeks. This was not easy, but it did the trick. I mention this because inevitably, sooner or later someone will make some comment about ludicrously high caloric intakes needed to "maintain muscle mass" and so on. This is just not true, and I can give you more details if you are interested.
As a parting shot - you're probably overdosing on protein.