Sounds like my DS, he never took much milk either, a constant worry even though he always gained weight ok. He also screamed the house down from 4.5 months old if he saw food. I stopped eating in front of him until 5.5 months just trying to hold off on the solids intro a little longer.
I wouldn't cut any milk feeds out yet, but you could increase the solids if she is crying for more. In general the advice is to ensure the milk intake doesn't drop whilst also allowing LO to self regulate the solids. If the milk drops too much then you could try cutting back on the solids to give milk the priority although this never helped my DS, he was a BIG solids eater but would never increase his milk regardless of the solids and just screamed at me if he couldn't eat the solids until he was full.
I didn't give any purees, BLW all the way here. I would follow her lead, if she wants some finger food go for it, if she finds certain foods too frustrating to eat then skip those for a little while and try something else instead. I avoided toast for a little while as I felt bread/toast would be spongy and stick to the roof of his mouth as you said, I was a bit worried about him choking on it actually, but after a short while I found he was very happy to eat the crust which was perfect finger food size. Then we moved on to toast fingers.
Steamed vegetables were always a great finger food here as were fruits (melon in wedges with the skin left on for grip, lightly steamed apple wedges).