I wouldn't want to risk the bike. It might be that the Egyptian customs at the Sudan border wouldn't be fussed about the dates, but we saw a huge compound full of confiscated vehicles at Cairo airport, and were told that they can be confiscated for fairly minor infractions.
We did extend our vehicle registration by 2 weeks at the Traffic Office in Cairo, although they initially claimed they didn't have jurisdiction because the original had been issued in a different governate (Libya border). This was in 1997, so the rules may have changed.
If you've already tried the Traffic Office and the Tourist Office for extensions, I'd try very hard to get out of Egypt before the registration expired, even if you have to go to Jordan and come back in.