When I service bottom brackets I always replace the caged bearings with loose bearings... this adds a bearing and removes the cage which is more often a cause of problems than losing a bearing in the frame. I have seen many broken cages that have scored the races and seen many bikes where the cage was installed backwards and caused an improper fit.

If you keep your bearing grease in a cool place it will hold the bearings in place during assembly and when it gets hotter here I keep bearing grease in my shop fridge for this purpose.

You can clean and grease the drive side cup without removing it and unless you are all thumbs getting the bearings placed should not be that difficult.

The bearing support is better with eleven 1/4 inch bearings than it is with cartridge bearings, and a good quality loose ball bottom bracket will last tens of thousands of km with regular service and run smoother.