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I can't help but think you have some impressive art for the mantle over the fireplace now ..

seriously..

lol
the pinion and ring gear are hard enough you can actually run the tip of one of the bolts that attaches the forks to the internal rods through between the gears without damage to them
.. the...

a twenty dollar angle grinder should have it cut in less time than a battery charge takes
bonus you can return the burned out grinder the next day ...

transmission re & re is much easier if you use an engine crane to lower it out and raise it back up into the car
I can't begin to imagine trying to shove an automatic back up from below by hand...