Second, if it is not convenient to say it directly, you can do so. You said to ask her to come on a business trip to help look after the house for a few days, and then you can stay with her when you come back.

Third, you can also invite her to dinner at home in the evening, preferably later, and then find a program to play. If it's late, you can stay with her, so that the guests who come for the second time will stay here.

As for the proposal, it's not a big problem for you to ask her again after you formally live together (you are not young, and she should be in a hurry). If not, you can pass on your cohabitation to her parents' friends and ask her parents to put pressure on her (this method should avoid scaring her away after you have lived together for a long time).