Hmmm, that may be an issue. Consider:
#1-Avid's drivers don't handle multiple clients well, so go to Windows Sound Properties and set the default playback device to the on-board sound card(Realtek?). This will allow Reaper to have total control of the 003.
#2-my opinion only, but Avid hardware is great with Pro Tools, but not so great with other DAW's(again, just my opinion)
Given the age of the 003, you might be better off selling it and buying a modern USB interface(RME, Focusrite, Presonus, etc)