Sounds like you're doing really well! Ignore Annabel Karmel and sleep programmes - I've had 2 sleepers and 2 non sleepers and think a lot of it is down to their temperament, and also had 3 big eaters and turns out my 7 month old is my first picky eater... So much is down to them and not anything you are doing right or wrong. All you can do is follow your instincts and try to listen to them and what they need.
Have you tried porridge fingers? Lots of good recipes if you Google and they have been my one go to for blw, especially with banana (even fussy ds4 eats that one), all the goodness of porridge with less mess.
For the blw I'd also strongly suggest finding ways to incorporate elements of family meals into what your baby eats. It's good for them to be eating the same as the rest of the family (or any adult who eats with them), and saves tears if they choose not to eat it. It's also a good incentive to cut back on salt or junk in your own food! For example, we make chicken stir fry, but before adding the sauce, take out some of the veg and chicken - voila, blw meal ready. Similarly for a pasta sauce with lots of veggies and beans - make sure the pasta is not to Al dente and baby can join you. Same goes for meatballs, or burgers, or frittata. I also buy those big bags of frozen broccoli and cauliflower florets, they're easy to prep and easy for babies to hold and gnaw on.
Then if you're doing purees, you can make a family meal again and just puree it - like a shepherds pie, or a chickpea curry with rice. On a really crap day, mash up some plain avocado and plain ripe banana or pear and you've done a meal, with no cooking 
If you have reason to suspect coeliac disease or egg allergies, these are both really serious and need to be confirmed, speak to your gp. If not, intolerances are really rare, but ironically you can increase the chances of them by cutting allergens out of your baby's diet. Babies who are not exposed to things like peanuts, eggs or milk in the early months of weaning have much higher rates of allergies.
Good luck and you are doing well! Have fun with it ☺️