Shimano 7 speed INDEX compatible rear ders have a different cable pull spec then their 11 speed stuff. So an 11 speed spec rear der won't index properly matched to a 7 speed lever, independent on the number of rear cogs.

BTW that braze on ft der (which I assume is mounted via an adapter as the Fuji never had a braze on tab) has a cage that is narrower then what the 6 speed chain really wants to fit through. So any small miss trim of the lever will result in greater chance for rub then what the OEM der would have had.

I suggest you spend some time studying the design aspects of indexed shifting more then move onto compatibility charts before spending any more $. Back when most here think indexing first came to the market (and that's 1984 for most but actually decades before from a few other brands including Shimano's Positron in about 1974) Shimano to better get the rest of the industry up to speed listed the 17 design points that an indexed system needs to be proper. Since then people have been trying to shortcut this and their bike have worked more or less for some amount of time and have degrading performance at a faster clip then a well matches system does. As the tolerances have been reduced by the "need" for more cogs in the same space the negative effects of a miss matched system are greater. Andy