First of all , congrats on your new baby.
Sometimes you have to find the right toys that really hold their interest. My TAG is almost 9 mos now , he was 5 mos when I got him and his favorite toys in the world are foot toys . I zip tied a sea grass basket to his cage and filled it with all kids of foot toys and he sits there forever digging through it. I also hide Nutri berries and almonds wrapped in cupcake liners in there so he finds little treats : )
To get him interested in playing in the floor I used a little wiffle ball and got him to chase it around. did not take him long to discover our toes and realized those are even more fun to chase : )
I was also afraid of him falling at first and kept the bottom padded with towels and made sure he had a little trail of perches in his cage so he could get around easily.
A far as engaging with her , you could try reading to her , even if it's just sitting at your computer reading your emails . I also would walk Cosmo all over the house showing him things and telling what they are and he really liked that. You might also try playing with a toy in front of her and then offering it to her . I have to do that if a toys scares him , usually if I play with it first then he will.
Their kinda like kids ...lol