Sounds so planned that it will come across as really unnatural and creepy. Personally I would just ask for the time, when she gives it, then start talking about how your early for a friend then if you want to use the opener you got you could say "actually you could help me out with something quickly" and use it and change the subject after. If you want to number close your going to have to chat and be yourself for longer than 20 seconds and be direct about it, say you seem pretty cool give me your number and we'll go for a coffee sometime or whatever you want to use. Asking a stranger if you can stay at her house if your friends have an argument is just plain weird.