If you are thinking of getting the K2 there are a few issues.
1. You fiance's son would need a letter from the other parent that gives consent to move the child to the US permanently, or sole custody of the child. Some countries are more strict than others when it comes to what you need. Canada for example, sole custody is not enough and a letter from the other parent or court order is still needed.
2. If the child leaves the US without advance parole then he cannot come back without you starting the all over again. The K1 is a 1 time use visa, he cannot come back on it, it cannot be used like a tourist visa.
3. If waiting until the EAD is approved to have him come later that could be 6-8 months. What is the point of waiting until the work permit comes? Is it again to visit or to move then after finishing school for the year? I've noticed that US schools do not line up with schools of other countries and they most likely still be entering mid year. This option would be the Follow to join with the K2 again the consent to move the child will be needed.
Tourist visas are not a given even if it is a child. You need to be sure to understand that if he is not coming on the K2 that he may never get a B2 to visit.