Well lets actually address your issue - why you think you need more power?....What is your voltage at idle - no accessories on/ then with Stereo on. Check at rear batteries and front battery.
The whole HO Alt trend is really something, most do not understand what actually takes place when you upgrade. 9/10 times upgrading means same size case, better internals which are wound for higher output with some efficiency loss at idle. No matter what there will be some trade offs just like a High Current Amp's power supply is wound different for higher output at low impedance - so is a HO Alt's stator and Rotor assembly.
By using the same case, installation is simple and direct bolt up. I would say very few cars can accept a larger case unit without major work. This is where "rewind" term comes in to play. The stator and rotor are wound differently, they basically create a larger amount of current due to how the unit is wound. Local shops do not usually wind there own parts and have facilities do this for them. The machines are expensive and large. So a "Rewind/Rewound" unit is the same as a HO Alt. They use the same parts internally.
I have had my hands in Alternators and Starters since I was 6 years old so I have a good idea what takes place in a rebuild. I would not recommend doing it your self unless you have some experience. Your unit is a very straight forward rebuild if just replacing all the internals, it requires some heavy soldering tools. Keep this in mind, even if you buy the parts to make it a higher output, most places will not warranty parts - so if you goof your buying another component. Probably easier to rely on an experienced shop