If someone missed KRIAT SHEMA in the right time (GRA, ect) due to not feeling well, or anything else. Are there opinions that KRIAT SHEMA can then be said until CHAZOT? Is THAT OPINOIN LECHATCHILA according to that opinion?
No, there are no opinions that Keriyas Shema can be said until Chatzos.
If the time is missed, then there is no way to make it up.
Keriyas Shema can be said until the third hour of the day. Although there are different opinions as to how this is calculated, nobody extend the time beyond the three hour limit.