Tracy L is correct. Windows of ANY flavor wouldn't do this for you. The software package running the network for Windows is the place to do this.
Generally speaking, once a "fixed" port accepts a particular connection and selects a "negotiated' port for the next connection, you are done. So the best way is to somehow intercept the port negotiation dialog so that the "pool" port that you actually use is the one you wanted to use. This means rewriting the TCP/IP connection layer software, which is guaranteed to not be trivial.
OR if the utility still uses .INI files or .CONFIG files, you would perhaps be able to modify the file to control the range of assignable ports so that when a connection comes in, you get that port next. You would need to know if the utility even supports controlling the "assignable pool" of addresses. If it does, you can do this from the configuration file. If it does not, you cannot do what you ask.
I am not 100% sure on this, but once a port has been negotiated, I think you are stuck with it for the lifetime of the connection. I studied this stuff some time ago and don't remember a sequence that says "switch to port X for the rest of this exchange." So catch the connection early or forget about it.