I don't think an ultimatum is the answer. I'm not entirely sure what else there is for you to do other than a freeze out. You are becoming the chaser with each move you make. Which isn't the worst thing if she likes you. Let's explore this.

A freeze out is meant for you to get the control back. So you can try to get her to chase you instead. Doesn't always work, especially on women you haven't slept with, but it does work at times. But what if you went the other route.

And I mean going old fashioned. Your dad and grandfather didn't know about pickup I'm guessing. Lots of them don't. So how'd they get the girl? Maybe, some old fashioned chasing.

Hear me out cause I know it's against PUA dogma lol. If you decided to chase her you'd be giving alot of power to her. Very risky indeed. But there is something that men who chase have over men who don't and try to get women to chase them. Persistence. And for some reason persistence can do alot for a man.

This is along the lines of direct game. It's about making your intentions clear. That you only want her. And "want the chance" to get to know her.

The other option I feel is to do a freeze out which could help or hurt your chances. And she doesn't have alot invested in you (emotional attachment, sex, money, living together, kids, etc) so it'll likely not work, but who knows. After a few weeks just attempt a new convo thread and see if you can start something with her.