As @chocolate already cited in the comment, despite the looking, this question isn't actually asking about usage of "though", but knowledge of the idiom
X からいい（ような）ものの Y, which roughly means "Just lucky that X, (otherwise) Y". I guess most native speakers would come up with this phrase when they've read to the part からいい.
For the possibility whether other choices could be true... well, purely grammatically speaking, C and B also have chances being "valid" (of course, only in very complicated situations that need a paragraph about the story so far). It however seems that they carefully chose wordings that none of other sound natural. If C were just ものの, the construction still works. Or it could be とはいうものの, in this case it'd mean "X, that said, Y" and at least make sense.
If you filled in C, the sentence would be like:
Despite being said that it was okay because the disease was detected in early stage, my life would be threatened if the detection were just a little later.
Contrary to expectation that it was okay because the disease was detected in early stage, my life would be threatened if the detection were just a little later.