It sounds like you may be over-feeding (but which I mean offering food too often, giving her the chance to be picky about when she eats). 3 solid feedings a day is quite a lot for a 5 month old, in my opinion. I kept mine at 1 solid feeding until 6 or 7 months, then got up to 3 feedings a day by about 9 months. In general, though, I don't think its helpful to try to force your child to eat. If she isn't hungry after a couple efforts, I would just give up until the next feeding.
Now, although I did the eat, play, sleep routine for both of my kids, I'm not convinced its necessary. Some of my friends routinely used milk to put their kids to sleep, and those kids started sleeping through the night at about the same time as mine. But, if you do want to follow that schedule, then you just need to bite the bullet. Pick a day when you can focus on your child and just don't offer milk before naps. Calm your child in other ways put hold firm on no milk.
How often is your child eating during the night? If its more than once or twice, then I would definitely try to reduce it. If it is only once or twice, then I think its up to you, and what you can tolerate. My first child's sleep habits started deteriorating, rather than getting better, around 4.5 months. He started waking up 5 or 6 times a night. So, at 5 months, I started waiting 15 minutes before going to him. After just a couple days, he started sleeping 12 hours through the night. My second child was still eating 3 times during the night at 6 months. So, I started to wait 15 minutes before going to him, and then comforting him until it was later than the night before when I fed him (so I was theoretically always making progress). Well, under that plan, my son very quickly went from 3 to 2 feedings, but I had a very difficult time getting rid of the two feedings. And, whenever he got sick, he backtracked. Anyhow, after 2 months of that I gave up. Then, at 10 months, my pediatrician told me I really shouldn't feed him during the night anymore. So, I let him cry it out. I spent much of the night in his room, comforting him in various ways, but he cried for almost the whole night. It was a very bad night, but, the next day he slept 12 hours through the night! There have been some other nights with some crying, but in general, he sleeps through the night now. Crying it out is hard, but I do think it works, and I don't think it harms the child in any way. As for the 45 minute naps, unfortunately, I think that's just common for this age. They will get better as your baby gets older. If you are still doing three naps, you might want to try to go down to two naps a day ... it may help. Good luck!!