Lets just have the new election count as the special election....there's no point in having a special election that's for a such a short term.
The problem is that the new District 1 and the old District 1 aren't the same. I could see having just a single vote only if the ballots were counted twice. In the first count, voters of Maryland, DC, and Delaware would join those of PA and NY for the special election for who would be Senator until January 6 (when the new Senators are to be sworn in) and the second count would be of the voters of just PA and NY to determine who would represent District 1 after January 6.