Hi, Im muslim myself but I am going to give an unbiased opinion as ever. Ive lived in 2 western countries and been to the middle east quite a lot, speaking from experience.
She might have feelings for you, and is likely to be in a position for long term marriage but not have considered it in your case because you are not religious. Whether or not she is in a position to be flexible about her religion, it doesn't matter, you will ruin her relationship with her family, the beliefs she grew up with, etc. forever, whether you like it or not. And you seem to be the most kind person also considering her feelings and her position within her family, I must admire that. But there is nothing you can do about it.
The reason she didn't like the other Asian guy is probably because she has grown up here and sees how different it is not to be in an arranged marriage, she might not even know this guy and is not willing to take that commitment.
If you are willing to take your relationship forward, and you want to have everything you mentioned to come true, you're going to have to convert to make her family (as a minimum) happy and trust me, whether you are pakistani or not, converting should mean the world to them and they should accept you if they truly understand the meaning of Islam. However, you got to be serious about whatever you do, converting is not just putting the status on yourself, it is about truly believing in the idea, otherwise there is no point.
So go around, speak to people in a mosque (speak to an Imam, trust me they are 10000x more approachable than you think, you can go there and speak in confidentiality and talk about your problem) and once you see how peacefully they are willing to help you and give advice, and you absolutely understand what Islam is and you are willing to convert, then you can take a step and talk to her about it.
I realise things can work out differently, this is as close as you might get. Many Asians here are Muslim, but might not take their religion seriously, and prioritize their background over the religion as a choice of their daughter's future partner. For all you can do to help, is converting, think about it thoroughly and know that whether she might perceive this as positive or negative, you are truly convinced you want to be a Muslim before you commit, and soon you will realize, it's the best thing you have done and you will be able to see how badly portrayed this religion is in the media.
Good luck. Peace out. Willing to follow this thread to further answer anything.