I think the medicine does a good job of controlling everything, but if they move you, I'd bet it is more likely to be sooner, rather than later. Or if it is later, you might want to postpone your trip, not your transfer.
I'm writing to make sure you've considered contacting some local IVF doctors to see if they are performing any studies. I had to pay for our IVF cycle (and was both surprised and shocked at times with what insurance would cover or not) but I've had friends that qualify for a discounted cycle by ...