Montessori schools are very expensive. If you know you can't afford, I would focus my energy on educating my daughter well in public school instead of debating the difference. Sending a child to an unaffordable school will do more harm than good. It sounds like your daughter is very bright, and she would very quickly pick up on the stress in the household due to the financial burden of her school. Also, if you send her to public school, you can use what available resources you have to send her to a camp, class, or online class to supplement her public education.
I would not worry about the public school's intial reaction that they won't advance her in reading. You have to keep in mind that many kindergarten parents are convinced that their children are much more advanced than everyone else's, and the teachers and administration aren't just going to jump at a request to grade skip a child they have never met. It sounds like your daughter is very bright, and it would be a good idea for her. However, you'll probably get better results waiting a little.
I would let her begin kindergarten without much issue. She will probably have a great time the first few weeks with the novelty of it even if she isn't learning much. During this time, I would volunteer at the school a little and get to know the teacher and principal. A few weeks into school, I would request that she be evaluated for giftedness.
Once that is complete, I would then start discussing grade skipping. You will get much better results if you've had a positive attitude and can back up your request with data such as class performance and and an IQ score. I think sometimes it's better to make short term sacrifices such as having your daughter in kindergarten a few months before skipping to gain a positive long term relationship with the public school. Remember that if your daugher is highly gifted, you will need to work with them many times. It's likely she'll need to do online learning, etc. in the future to keep learning. It's very possible to get great results from a public school education, but I think the key is to maintaining positive relationships.
