I have used several conversion units and have not found any that will shoot as well as a good .22 pistol or revolver. They were originally intended for inexpensive military training for those armed with the .45 pistol, so they didn't have to shoot any better than the average GI .45.
If you want to retain some of the feel of the 1911 type, Ruger makes the 22/45 which has the grip angle of the 1911 and will run well under $400. Other alternatives are the S&W .22 autos and revolvers; a used K-22 would be a very nice gun and should run under $400.
Jim