David,
Typically the bronze outer casing is the same length as the rubber insert as you would never have unsupported rubber nor would you press just the rubber portion into the shaft log. It may be that your inner rubber has expanded past its bronze casing or shifted slightly overtime but it should be minimal, just enough to fool the eye. I have used this method for bearing and bushing extraction and replacement on a myriad of automotive, motorcycle and marine projects. My only cautionary notes are;
1.) Use the largest diameter threaded rod you can that will still allow for a nut on the inside. One half inch rod is probably just too small but you could try. Grind the inside nut down if you have to, it is OK if it spins on the rod instead of the outer one when you turn the wrench, it will still draw the bearing out.
2.) Use at least two washers on each end, three is better. One washer by itself will bend. The inside washers need to fit very close to the inside diameter of the log. Grind them if you need to so they just fit inside.
3.) Grease the rod liberally and avoid a galvanized one if possible as it creates more drag and friction on the nut.
4.) Don’t forget to remove the set screws if your shaft log has them.
5.) These cutlass bearings have a pretty tight interference fit which is exacerbated by years of corrosion, there is a good chance you will need to heat the shaft log.
6.) The ‘waterpipe’ in the drawing must have its edges perpendicular to its length. You cannot hack a pipe off with hand saw or power cut off tool. I am usually successful getting a premade pipe nipple of the appropriate diameters and length from the plumbing department at Home Depot. You can take a small square from the tool department over and check some in the bin with it.
-Mike