What's going on here? I can't believe it's supposed to be so. What can I do? Is it possible I have a non-standard A1200?
No it's standard, might just be the Indivision AGA scandoubler that has a crack in the mount socket?
I suppose there's no way to replace the connector? Do I have to consider this Amiga a total loss?
Just desolder a old PCMCIA from and old laptop and resolder it on your amiga, go to your local electronics dump and pick up a few old laptops and find one that fits

Last question: Is there ANY way to disable the Blizzard 1230 Mk.II at boot WITHOUT having to physically disconnect it? 
Use the "2" key when booting to disable it

//som99