You would have to throw in an extra draft pick to get Washington to eat whatever portion of the contract you need them to like the Rams did for Denver.
No cap expert but the WFT site I read it off says you can't do that with a franchise player. It's by design they want teams to work out contracts or trade guys before they franchise them. Once they're franchised they make it intentionally harder to trade.
Ironically one of the "test cases" on that was Von Miller in 2016. The Broncos tagged him, he waited until the last possible second to sign it, they made it clear they weren't going to trade him so he signed a 6 year 116 million deal that he's still on now.
Could be wrong but the side I read specifically said whoever would get Scherff MUST have room to take on his entire remaining franchise tag amount.
Apparently many wanted them to trade him before the season for that very reason they were pretty certain he wasn't going to sign another deal with them.