There are several hints already that this happens a few years after the 5th HGW. Rin was mentioned to be in the Clock Tower. El Melloi II has Iskandar's catalyst so 4th HGW happened. Francesca also mentioned about the Einzberns being too uptight in every HGW, using a new class in 3rd, using a major hero in 4th and making another major hero insane in 5th. Orlando even specifically mentions the 5th HGW and Berserker.
There's also
And we have DAs and DAAs around this time but I doubt that's a tie-in to Tsukihime.