Nice pictures, they tell the story
1) For whatever reason you need to remove the armature from the case end. yes?
That's important, since if the problem were the start switch and it can be removed from the side....
Or the stator winding......
Then you leave the armature installed in the end plate, stuck onto the pump shaft.
Lets assume you can't fix the motor problem with the armature installed... The pump shaft looks to be made from a soft material like brass or copper. So worst case you need a piece of brass plate and tubing to create a new T shaft. Wouldn't it be nice if that tubing were normal copper pipe....?
I imagine a puller like this
-a plate with 4 legs straddling the upper housing.
-In the midddle of the plate is a hole
-Thru that goes a threaded rod.
-cross plate and bolts attache end of rod to pump
-nut and washer attach rod to plate.
-Tighten nut to remove pump "T" shaft from motor.
Alternately, you drill and tap a large thread thru the T top, (perhaps reinforced with a helicoil)then screw a bolt in, jamming against the armature shaft, and so pull the T shaft loose from the armature shaft. No force applied to the armature body, motor end plate and T shaft plate ends this way. You'll have to seal the hole later via soldering a plug on.
Note, brass/copper expands faster than steel, so heating "T" to 300 or350F may greatly ease it's removal.
I'd heat the T shaft up with a micro torch, not a lot tho', and try to start wiggling it a bit while a pulling load of 100-200 lbs is on it.
That may be all that's needed, or...it may be corroded on, and need to be replaced.
It looks to be a LOT easier to fabricate a new T shaft than a pump housing.