You can transfer morula just like blastocysts into the uterus. If you want to put them in the oviduct, you will need precise ultrasound techniques and specialized equipment. What is your aim?
Yes, we want to study second lineage differentiation, which happens by day 9.
I think the great challenge in tranfer at day 4 is to synchronize the recipient to the embryo - if the uterus is not "ready" for the embryo, because ovulation occured a little later, the embryo cannot survive. Now we will transfer at day 5, day 4 is just too tight a timeframe (oviduct passage ends at 3.5).