Most regreaseable motor bearings have plugs on top & bottom. The proper procedure is to remove both plugs, pump grease into top port toll it flushes out the old grease from the bottom. close ports. Forcing grease into one port only will not grease bearing, but force grease into the motor housing. Just the way I was taught during my 35 years as a maintenance supervisor.
Good procedure fixit.
I have replaced bearings on a number of motors which had zerks and were greased on a timed basis.
When I opened them up I found they had sealed bearings and the grease was just forced out the bottom or into the stater.
I like to use sealed bearings and remove the zerks.
There is usually one or more springs which press against the brng on the back of the motor. They are needed.
When using a puller make a plug to go between the motor shaft and puller screw so the motor shaft isn't damaged.
I've had to do machine work on a number of rotors which had the centers damaged and it took time to clean them up
and make them true to the shaft center.
If the brng has spun in the motor end cap and worn the sliding fit you may have to sleeve that fit.
Measure the bearing fits in the end caps cause now is the time to fix them.
These small motor bearings have only 2 tenths interference to the shaft.
If the shaft diameter is 1" then heating the bearing just 60deg above ambient will expand it 4 tenths.
It is best to not heat a sealed bearing above 120deg or the seal may be damaged.
Some people use a toaster oven or you can set that Christmas ham aside and use the big oven to heat the bearings.
As others have said, it's a good idea to freeze the shaft.
Also, when installing the bearing I try to have the shaft solidly standing vertically if possible.
I also like to rub antiseeze inside the bearing and on the bearing fit. You can thin the antiseeze with a light oil.
It has to be spread so thin that that it's almost invisible as it it will take up space and change the brng fit.
Antiseeze will make the bearing easy to pull next time if it's applied really, really, thin.
Many of these motors have a inner shield that has to be placed on the rotor "before" seating the new brng.
Big mistake if you forget those.
The brng must be held firmly against the shoulder of the shaft until it has seated so you'll need a insulator
for your hand.
I've rambled on till it's embarrassing. Hope some of this helps.
Jim