Almost. PBR is a feature specific to Cisco IOS (routers and switches). The ASA has the means to accomplish what you are attempting to do. The ASA calls it "Policy NAT".
Policy NAT is simply using an access-list within a regular Static NAT or Dynamic NAT statement. This gives you much more flexibility in defining "what" you are trying to NAT. In regular Static/Dynamic NAT, the only criteria you have to specify what you should NAT is the source IP. With Policy NAT, you have an access-list, which allows you to use Source IP, and Source Port, Destination IP, Destination Port, and Protocol.
On second read, however, it appears you aren't necessarily concerned with NATing, but with Routing. That is rather odd. Does the connection to port 1000/2000 that needs to go out interface A go to a specific IP or Network? Normally ports aren't what is used to distinguish where traffic goes. If you could provide additional detail in what you are trying to accomplish, I'm sure we could think of something to accommodate.