My dd is going to be 1yr on Friday, and we have been dealing with this exact same issue since her 9mos check-up. Despite introducing solids, she did not gain any weight between 6 and 9mos. She has actually fallen off the bottom of the weight charts. At 12mos, she is only 16lb, 6oz.
I looked at your schedule, and do not see anywhere to add another snack. I would also keep the 3:30pm bf instead of a solids snack.
At 9mos our ped ok'd protein and dairy, so here are some of the things we added to her diet...
Pureed lentils (She really likes them mixed with carrots.)
Dark meat chicken pureed in pan juices (including the fat)
Cheese, cheese, and more cheese! (She loves the prewrapped American cheese slices, but has eaten just about every variety we have offered.)
Yogurt (I don't give her baby yogurt, but rather the highest fat whole milk yogurts I can find the store - she loves Dannon La Creme. I also give her Stonyfield Farms whole milk vanilla yogurt mixed with pureed fruit. Yoplait also makes a custard style yogurt that I am going to check the calorie count on.)
Cream cheese (I started lacing her veg purees and oatmeal with cream cheese for a while, but she also likes it on bagels and banana bread.)
Pumpkin custard made with cream instead of evaporated milk (I used my pumpkin pie filling recipe.)
Cheesecake (She tried it and liked it, so I am going to make a cheesecake for her birthday.)
Hummus (I make it myself so there are no preservatives.)
Mashed potatoes laced with butter, sour cream, formula, and sometimes cheese
Any pureed veggie with shredded cheese mixed in
For now, I wouldn't worry about puree vs. finger food. We offer both at every meal unless we're having a meal where I think she'll eat a good chunk of whatever we're having. Dd is still eating puree at 12mos, and as long as I am getting food in her and she still has interest in finger food, I am not going to worry about it. And there's nothing wrong with hiding things they won't eat in things they will. Dd won't eat pureed beans or meat separately, so I mix them in her favorite veggies. I assume you're already making his cereal with ebf or formula, but if not, that's something else you could do.
This has been odd for us as dh and I are relatively healthy eaters, and I have had to change my shopping mentality completely. I know how stressful this can be. Feel free to pm me if you want to discuss this further.