High Calorie Foods for Toddler Weight Gain

I spent hours doing some research into high calorie foods that can help me out with Sasha's underweight problem. She's finally eating, and I want to make sure that every bite counts.
I'm no expert. Just a desperate mother of a toddler who won't eat and is losing weight instead of gaining. Here's what I found and what I am doing.
First, I had to make sure that she's getting all the vitamins and nutrients she needs. She is now agreeably taking a half of a chewable flintstones vitamin every day so I don't have to worry about those nasty vitamin drops. The flintstone vitamins have more kinds of vitamins in them anyways. However they are lacking in CALCIUM, so I still have to make a special effort to get calcium into her every day.
Second, I needed to know exactly how many calories I should be getting into her every day. For that, I thank this website: http://www.silverscriptwellness.com/topic/calneed
I used it to calculate how many calories Sasha needs each day. She weighed 18lbs 8oz at her last doctor visit, and she is 30 inches long. Therefore her calorie needs were as follows:

She needs at least 595 calories to maintain her current weight and activity level.
Of this, 395 calories are required to meet her body's basic energy needs. That amount (your resting energy expenditure) is what she'd use up if she did nothing but lie in bed all day.
To gain about one pound per week, you'll need to bump up to 1,095 calories per day.

Next I tried to calculate how many calories she was getting. This was hard. After searching around I found this really neat website: http://www.calorieking.com/foods/

It told me the amount of calories in different foods, but I could get the amount of calories in different sizes so it was actually really helpful.
Let's see, she eats about 1/2 cup of brown rice mixed with lentils a day (108 calories), and about 2-3 juice boxes (100 calories each). Plus she nurses about 4-5 times a day (about 60 calories per nursing session). I calculate a total of 548-708 calories a day. Barely enough to maintain her weight. Not enough to gain any weight at all. She needs MORE calories. Much more. But she's not going to take more bites so somehow I have to find ways to pack more calories into the bites she does take.

I spent a few hours trying to find the most calorically dense foods. To do this I made a chart of the amount of calories various foods had per ounce and also per tablespoon. This is what I came up with:
food per oz, per other measurement
tofu 41,
whipping cream 98, 52/tbsp
butter 204, 102/tbsp
half&half 40, 20/tbsp
sour cream 61, 26/tbsp
milk whole 19, 9/tbsp
breastmilk 20,
avocado 45,
brown rice 32, 108/half cup
potato 26, 57 half cup
sweet potato 26, 57 half cup
lard 252, 126 tbsp
flaxseedoil 251, 120 tbsp
oberweis choc ice cream 79, 230 half cup
jelly 71, 50 tbsp
peanut butter 169, 95 tbsp
carnation 103, 130/packet
whipped cream 73, 8/tbsp
Hershey's Ready-To-Drink Milk, Chocolate, 2% Reduced-Fat, 8oz box 200 calories!

Basically it seems that fats are the most calorically dense foods I could think of.
Sasha eats mostly brown rice all day every day now, and chugs down a few juice boxes. I am thinking of doing the following:
1. Replace a juice box or two with higher calorie juice box containers of other stuff than juice, like chocolate milk. It has to come in a juice box or Sasha won't drink it. Hehe!
2. Butter everything.
3. Replace milk with half-and-half, or in some instances, even whipping cream. These are very very high in fat. Babies and toddlers do need fats in their diets, especially skinny little ones. I just have to be careful to make sure she's getting protein and carbohydrates in her diet as well so she's not on an all-fat diet.
4. Offer the occasional spoonful of peanut butter or even jelly/jam if she'll take it.
5. Ice cream and whipped cream! I got a can of that pressurized whipped cream and had my older daughter try to teach my toddler the joys of whipped cream. So far, unsuccessful. She giggles at her older sister with a mouth full of whipped cream but won't eat it herself...yet.
6. Make a super thick high calorie very rich drink with 8oz of half&half and some carnation instant breakfast. If you can get this into your toddler, there's 445 calories in this. Good luck. This tastes like heaven. It tastes like melted ice cream. Sasha wouldn't take more than a few sips of it.

I'm sure there's plenty more ideas but that's all I can think of for now. Basically don't let any bite go into that toddler's mouth that isn't dripping in butter, cream, or an oil of some kind.
These are the desperate measures of a mother of an underweight toddler who is losing weight. Once the weight starts to get closer to a normal range, I'll stop lacing all her foods with fats.

Please, if anyone has any other ideas or suggestions, or anything that has worked for you in a similar situation, please feel free to leave a comment. Or commiserate and share your experiences.