You likely can't claim the border guard seeing it, as people do all sorts of things with fancy flights and it's up to the traveller to ensure they're doing the right thing. You could have had a return from Australia to Los Angeles, then inbetween flown to South America and back, and wouldn't have overstayed, so it's not on the border guard to check this.
As for being allowed to leave - yes, there's no exit immigration check in the US. They're unlikely to fuss or cause you problems. However, getting back in will be difficult.
Some of the consequences of overstaying a visa are:
- Overstays may be barred from returning to the US for ten years or three years depending on the period of overstay
- Overstays may be further restricted from Extension of Stay or Change of Status
- Overstaying will void your existing visa
- Overstays generally are unable to obtain a new visa except in their country of nationality
- Overstays may not be able to Adjust Status in the U.S.
In addition, let's say you accidentally cause a crime in the US. Traffic accident. Involved in a robbery. You're an illegal alien at this point, and that'd likely lead to further issues. Your insurance will be void.
However, don't think that the lack of exit immigration will let you 'sneak' out - they'll still track your entry/exit flights and know when you depart. So it'll still be recorded as overstaying. Many many examples are easy to find with googling eg ' how do they know?'.
So yes, you could do these extra few days and hope all is good. Or you could apply for an emergency extension at an embassy/consulate (don't know how long this might take). Or you could, and unfortunately probably should change your plans.
Note - hopping across to Canada/Mexico won't reset your 90 days either, sorry :/