What are the alternatives to the "EBAM" products offered by SWIFT that would allow me to manage bank accounts electronically?

There are actually two parts to the eBAM concept that SWIFT has developed. The first part are the file formats themselves that allow a corporation to electronically send bank account management information back and forth with their banks. The second part is the connectivity portion. The SWIFT Corporate Access portal is certainly one way that these messages can be transmitted back and forth in full security, but technically, the eBAM message formats could be exchanged back and forth over just about any electronic channel.
Corporates will have choices when they determine how best to communicate with each of their banks, but the eBAM file formats themselves are almost certainly the best way to send the data back and forth.
As more and more corporations get onto the SWIFT corporate access, it will likely become the communication mechanism of choice for large corporations. There are many ways for a corporation to get connected to the SWIFT network, and some options are rather inexpensive.