I'm late to the convo, but just wanted to say it sounds like you're making great progress!
We had some problems with Owen wanting to eat too. He was one hefty little babe until he got mobile, and then he was too busy to want to eat!
The best way to get food down him was to really punch the dense calories - this was hard at first for me, since I'd spent about 5 years training myself NOT to add calories to my food! LOL! But, it helps to give them really calorie dense foods to that what they DO eat gives them max nutrition.
One thing that worked well with Owen was fruit smoothies made with full-fat yogurt. He could drink it down, which was esp. fun when he was just learning to drink from a straw around your LOs age. We also added full fat cream cheese to EVERYTHING! Some of his first finger foods were toast soldiers with cream cheese, and mini-waffles with cream cheese. He still loves both of those things.
You're on the right track, making sure solids before milk. At about 1 year old, they should be down to basically 16 oz. of milk/day. More than that they fill their little tummies and don't want to make room for the foods they should be eating.
And I totally agree with giving them spoons/bowls to play with. PP is right - they need to learn to use them, and it makes mealtimes more interesting for them! Fun sippy cups with favorite characters might help too. Another great idea a mom gave me was serving food on toothpicks! That might be too much for a 1 year old, but something you could try at 18-24 months. Anything that makes it more interactive seems to work with 'busy' kids. Now that Owen is nearing 2, we let him feed us a bit when he starts losing interest in the meal - so one forkful in his mouth, one in ours.
You're doing the right thing, following your instincts! I think the BW philosophy is right on: never make mealtimes a battle. Sometimes that means my LO only has a few cheerios and some yogurt for a meal. But with regularly scheduled meals and snacks, I know he'll get the food later in the day at some point.
Last thought - make sure those 1 am, 5 am cries aren't from habit instead of hunger. A good filling snack before bed may help with that problem. Carb/protein combos are the best for that.