Syntactaphasia

Open Table last week sent me a confirmation of a restaurant reservation.  It included the instruction that we would be cancelled "unless you call before 10 am on the day of your reservation". 

Um:  suppose our reservation is for 2 pm Thursday and we receive this message on Monday.  Clearly (yes?) a call at 955am Thursday is sufficient.  But what about a call at 1159pm Wednesday?  Or, come to think of it, a call on Monday just after we receive the instruction message? IOW, does the call have to come on the same day of the reservation?  Or is any time "before" enough?

Would the answer be different if the reservation was for next year than it would be for a reservation in the same week?

More to the point, is there a non-clumsy way to restructure the message so that it removes the ambiguity?  Or rather, two ways, one of which allows for an early message while the other does not?

Update:  David A  says:

How about judicious use of parentheses:

before 10 am (on the day of your reservation).

Or,

before 10 am on <>

Or, I think you might be overthinking it a little.

David S adds:

 Aargh.  Eat someplace else.

 Me, I'm also still worrying (I may have written this one before) about the line in the local fishwrap that said "of those who did not die in the first year, even more died in the second."   Well yes, and of those who did die in the first year, none died in the second.