Your plan to have her use her Esta to enter with the intent to adjust status is a big no-no. Maybe this was also why her F1 got denied, they suspected that she would use this non-immigrant visa with the intent to adjust status?
If she gets an Esta, she can visit you (at the discretion of CBP of course) and you might even get married, but have her leave the US after her visit and apply for the CR1. Or you can of course do the K1 if that’s what you prefer.
No easy shortcuts in Immigration, you will want to do this the right way.