An 'Autoland' is
not the same thing as a Cat 2/3 approach. The aircrfat doesn't care whether visibility is good or bad, or whether the ILS is a CAT 1 or a CAT 3 installation, if you tell it to do an autoland, it will try and do one to the best of it's ability. It's ability to do so is affected by the exmaples of criteria you mention: G/S angle, no offset LLZ etc.
CAT 2/3 approaches don't use a 'special' kind of ILS system - it's the same bit of kit, just supplemented with runway lighting, back-up power, monitoring, an accurately surveyed approach, ATC LV Ops etc etc.
So as long as the technical requirements for a safe autoland are in place (and you mention a few of them) as defined by your regulator/company, you don't need a 'CAT 2/3' ILS to do one - if you are conducting the approach to CAT 1 minima (as you should be), there ought to be no problem letting the aircraft fly to touchdown, since you will have the necessary visual references to disconnect the autopilot and take control if you don't like what you see (just like when the FO's flying
).
Be sure to apply any other relevant procedures, such as performance corrections to LDR or GA WAT limit, which may be associated with autolands, though.
If in doubt, ask a company training captain.