I will like her message "We're landing..." and respond with something like "They must really like you".
Exchange 2-3 flirty messages and say "We definitely have to meet, when you'll be here".
Then write to her before 30th and make plans.

But I'm feeling she is the type of girl who looks for attention and doesn't want to meet.

Thank you for the feedback! First soft close was "It's even more fun in real" but she responded negatively.
I was trying to get her to reply with more investment before the next attempt to close.

"If you are too scared I understand", "Don't think too hard"

"I can give you my proffesional opinion about that over a bottle of wine"

She seems convinced to meet with you. In my opinion no need to game there. I'll write something like "Prosecco it is. When are you free"

In my opinion it might be that she really don't have a time to meet sooner.
I think that by pushing it's very little chance for success. It can only make you seem needy.
I'll wait messaging her a little bit and try to meet when she'll be free.

You can go with humor: "Us having wedding next week". Then you can continue acting like you are in marriage.
Don't know if this is the best answer, but that is something I would do.

In my opinion, you should consider changing style, clothes and hairstyle and do new pictures.