is this pbx producing the data in a continuous logging fashion - spitting it out as the calls come in or go out? I assume it is - that's how mine does it.
You could look at serial data loggers. I haven't seen any with multiple output ports.
a micro with 3 serial ports and sufficient storage could be made to work.
alternatively, if there is room for a PC, you could set it up with extra serial ports, write a little program that stores the data coming in on the pbx port and then spits it out on the other two ports when some condition is reached on the other end (i.e. a machine ready for input). Of course, a cooler solution would be to make the PC drop it into a webformat and allow the use of a web browser to get the data. In either case, I'd run linux on it.