I would under no circumstances allow class of service to interfere in flight connections for EWR-DCA. OP's intl. Business ticket will ticket into domestic F where it is available. This can be anywhere from a 25-40 minute flight and there is largely nothing F about F other than the seat.
Bearing in mind that WX and ATC problems are the most common cause of problems on the mini-haul to DCA, the better backup is Amtrak.